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CHAPTER TEN -CONCLUSIONS
10.1 Introduction
This PhD research was designed to answer the research question: “How is the mining
regulatory framework in Western Australia being implemented legislatively to assure
environmental protection during the mining life cycle?” The focus of this study was limited to
examining environmental compliance by analysing the regulations that manage two types of
minerals, i.e. uranium and coal. The research did not focus on the economic or social aspects
of sustainable development principles concerning mining. Many other important issues
related to the environmental protection of mining operations in WA were outside the scope of
this research project. They include examinations of the regulatory framework of the petroleum
and gas industry, the longitudinal impact of mining on ecosystems, and biodiversity to name
a few examples. This thesis concentrated on only one, but a critical aspect of mining
operations, namely what kind of regulatory framework is put in place, and how it is being
legislatively implemented focusing on Western Australia. The State of Western Australia has
a strong economy predominantly supported by mining. For example, the revenue from mining
Royalties collected accounted for 29% of GSP in 2016 - 17. (Government of Western Australia:
Department of Jobs, Tourism, Science and Innovation, 2018, para two. Further, WA's gross
state product (GSP) of $247.7 billion during 2016 – 17 contributed to 14% of Australia's gross
domestic product (ibid).
There are many examples across the world, and in Australia where the income from the mining
is enriching the economy. The economy of Queensland is similarly structured. Mining
contributes significantly to the economies of Canada and many Latin American countries, such
as Chile, Peru, Argentina and Mexico. Developing countries in Africa also heavily depend on
mining to support national economies. Further, mining is also an essential activity in large
economies, such as India and China where the mining industry employs millions of workers.
In this thesis, I identified positive elements of the regulatory framework such as the coverage
of wide range of mining-related subjects, effectively collecting Royalties, and introducing
mining rehabilitation legislation to address the legacies of over a century of mining as recent
as 2012 by introducing the MRF Act. Secondly, I provided evidence that the MRF Act has
limited jurisdictional power, and has no authority over the State Agreements. Thirdly, I
identified several issues that have contributed to the weaknesses of the mining regulatory
framework. Fourthly, I observed that some key legislation such as the Mining Act 1978 had
been developed through a ‘legislative evolution’ of over 100 years, without an overall direction
and coordination. Fifth, the findings revealed that the MinReF consists of legislation with
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inherent weaknesses such as unclear demarcations and overlaps of legislation, the
ambivalence and dichotomy of the mining regulatory framework. Sixth, I identified that the
MinReF and the agencies that are responsible for implementing various legislation had not
developed an adaptive capacity to cope with changing needs and legislative shortfall such as
how to rehabilitate 17,000 abandoned mines in Western Australia. Due to gaps and
deficiencies of the current mining legislation, remaining abandoned mines cannot be
rehabilitated during the present generation. The implication is the State of Western Australia
has breached the central principle of sustainable development—the principle of
intergenerational equity (United Nations General Assembly, 1987, p. 43) as the liability of
rehabilitating 17,000 abandoned mines would be pass on to the next generation.
As a contribution to new knowledge and developing new theories, I proposed a new theoretical
framework—ADMINREF to establish an ability to adjust and make improvements to the
MinReF in response to the changing needs of society to cope with the consequences of the
current legislative shortfall through innovative policy discourses. Finally, this thesis put
forward a series of recommendations to address the gaps and weaknesses of the MinReF
based on the findings of this PhD study.
10.2 Addressing the research question and objectives
Further to the primary research question, this PhD study included four research objectives,
and they have been addressed in chapters seven, eight, nine and eleven respectively. The
research question and the objectives were addressed by carrying out an analysis focusing on
two case studies and reviewing the MinReF in WA. To address the research question and
four objectives of this study, I used three sets of data—two sets of primary data and one set
of secondary data which included the information extracted from an extensive literature review.
The first set of primary data included the Federal and State legislation covering mining and
the environment as they are considered primary data in legal studies. The second set of
primary data was collected from a group of research participants (n = 16).
10.3 Research objective one
I answered the first research objective by identifying the strengths and weaknesses of the
MinReF in Chapter Eight. While analysing the framework, I noticed positive elements of the
framework such as the extensive coverage of mining-related subjects and the implementation
of mining rehabilitation legislation (MRF Act) enacted in 2012. However, the downside was
the MRF Act had not addressed the mine rehabilitation ‘problem’ that comes under the State
Agreements (SAs). 17,000 abandoned mines are a part of the legacy of a century over mining
operations in WA. The MRF Act has limited jurisdictional powers and cannot be applied for
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SAs that have been developed to support large-scale resource projects. I argued that such
issues have occurred due to the dichotomy of the mining legislation as a result of adopting
two separate systems for approving and managing mining projects under the Mining Act and
the State Agreements (SAs) respectively. I also found evidence that the two systems are
engraved within the mining regulatory framework due to historical factors and gaps and
deficiencies of the framework. I noticed these two systems are against the governance and
equity principles of public policy.
10.4 Research objective two
Chapter Seven was devoted to address the second research objective, by developing two
case studies using qualitative research methods. The two comprehensive case studies using
qualitative research methods were developed based on an investigation to ascertain how
environmental regulations have been implemented legislatively during the approval of a
uranium mine project in the first case study, and key issues about the approval process. In
the first case study, I identified issues about the validity of legislation used to approve the
uranium mine. The conclusions from the case study confirmed the problematic nature of
Yeelirrie Act 1978 utilised to approve the mine. Further, I discussed how the Ministerial
authority overruled the scientific evidence against the approval of the uranium mine on
environmental grounds including the adverse impact on biodiversity.
The second case study examined the environmental compliance of coal mines during the life
cycles of mines located in the Collie Region in South-West West Australia and managed
through a set of unique legislation called State Agreements. In this case study, legislation and
regulations relating to the issuing of mining tenements, the provision of water and land access
were also analysed by examining the role of the State’s mining legislation and regulations. In
both case studies, I focussed on environmental compliance. The analysis of the coal
operations in the Collie Region provided evidence that the use of State Agreements has not
assured environmental protection as at the end of the life cycle, many abandoned coal mines
have contributed to adverse environmental effects. The findings of both case studies revealed
flaws in the legislation used.
10.5 Research objective three
I addressed the research objective three in Chapter Nine, by identifying the diverse nature of
the term ‘best practice’ and how it had been used in Western Australia by examining the ‘best
practice’ models of two key agencies responsible for mining and environmental regulations.
Secondly, I presented five examples of Australian and best practices of innovative approaches
to ecosystem restoration and mine rehabilitation. The five best practice examples also reflect
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key elements of ‘corporate social responsibility, and ‘licence to operate’ introduced in Chapter
Three of this thesis. Five examples provide new insights and suggest opportunities available
to ensure environmental protection through ecosystem restoration and mine rehabilitation
work external to the government regulations.
10.6 Research objective four
I addressed the fourth research objective in Chapter Eleven, by proposing ways and means
of improving the MinReF to assure environmental protection. I proposed seven
recommendations to address gaps and deficiencies identified as an outcome of the analysis
of the MinReF. One of the critical gaps I found in the regulatory framework was the limited
jurisdictional power of the MRF Act which is incapable of addressing the ‘problem of mining
rehabilitation’ across WA.
10.7 Summary
This thesis describes an analysis of two case studies supplemented by the findings of a review
that examined the strengths and weaknesses of the mining regulatory framework in Western
Australia using three types of data sets. The overall findings of this PhD study were identified
under seven thematic frameworks. They are: (i) inherent weaknesses of key legislation; (ii)
unclear demarcations and overlap of legislation; (iii) ambivalence and dichotomy of the mining
regulatory framework; (iv) lack of coordination of mining regulatory framework and multi-
agency roles; (v) absence of an apex agency to coordinate mining regulations; (vi) delays in
introducing environmentally-centric legislation; and (vii) lack of adaptive capacity.
The seven key findings represented three critical characteristics of the regulatory framework.
They are (a) the “fragmented nature” of regulatory functions; (b) the way the legislation and
regulations under the MinReF have evolved through a legislative evolution over a period of
160 years and are now implemented through multi-agencies, and (c) the absence of an apex-
level agency to coordinate the regulatory functions effectively.
Though this research project identified significant gaps and deficiencies in the current
regulatory system, they need not be considered as a negative evaluation of the mining
regulatory framework in WA. If public policy makers look at the findings of this thesis, they will
see opportunities to improve, without merely focussing on facilitating non-renewable resource
extraction which is not sustainable as it has an end date in the future. Although this study only
focuses on the regulatory framework regarding coal and uranium, the findings provide new
and independent insights, and they supplement existing knowledge on the effectiveness of
the overall mining regulations in WA and elsewhere. Insights gained from this study would be
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useful to examine other mineral and petroleum (gas and oil) regulations that are not addressed
in this study. Though the research and the findings are focused on WA, the methods used to
conduct the research could be useful to address both national and global problems relating to
environmental regulations concerning mining.
During this research project, I found that the Departments of Water and Environmental
Regulations provide transparent information on environmental impact assessment submitted
by companies for public perusal without deleting any information. Further, the Department of
Mines, Industries, Resources and Safety provide access to open access database (MINDEX)
via the agency website that provides mining company details and environmental reports.
These initiatives are like flash-lights while walking in the dark passage of mining history in
Western Australia. These initiatives could also be described as evidence that key regulatory
agencies have begun to embrace the concepts of ‘corporate social responsibility’ and ‘licence
to operate’. They are indeed good signs after the legacies of 100 years of mining in WA.
Concerning theory development, this research contributed in three ways. First, it examined
relevant theories such as ‘Bureaucracy’ (Weber, 1952, 2015); ‘Discourse Analysis’ (Stubbe et
al., 2003; ‘Public Interest Policy’ (Ogus, 2004 & 2004a);’ Legal Doctrines’ (Hoecke, 2013), and
‘Regulatory Design Principles’ (Gunnigham and Sinclair, 1999) as investigative methodologies
to analyse the environmental legislation and regulations come under the MinReF. Second,
this study contributed a new theoretical framework—Adaptive Capacity for the improvement
of the Mining Regulatory Framework of Western Australia” (ADMINREF) to eliminate gaps and
deficiencies of the MinReF by adopting innovative policy approaches (Chapter Eight, Figure
8.4). Finally, this thesis includes a series of policy recommendations to address the current
gaps and deficiencies of the MinReF, and they are included in Chapter Eleven.
In summation, this thesis focused on two case studies supplemented by an analysis of the
strengths and weaknesses of the MinReF in WA. The summary of the findings was compared
using a theoretical approach that describes key elements of adaptive governance with the
findings of the analysis of the MinReF. The comparison of the summary of the findings against
the key elements of the adaptive governance principles is presented in Table 8.4.
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CHAPTER ELEVEN – RECOMMENDATIONS AND FUTURE RESEARCH DIRECTIONS
11.1 Introduction
From a sustainability point of view, mining is a very contested economic activity as it inherently
uses non-renewable resources and impacts on the social and environmental health of the
human and ecological communities where it operates. Mining, however, will continue into
future driven by the need for mineral, gas and petroleum to improve the quality of life of current
and future generations. However, insights gained from past activities, identifying mistakes
made, and examining the strengths and weaknesses of the current practices are of paramount
importance to create a better future to ensure that future generations would have the same
benefits of the present generation as practicable as possible.
This research investigated how mining regulatory framework (MinReF) in Western Australia
(WA) is being implemented legislatively to assure environmental protection following during
the life cycle of mining through an in-depth analysis of two case studies, and a general
investigation of the regulatory framework. The research question and the objectives of this
PhD research examined the legislation, regulations, and other administrative tool come under
the MinReF in WA by focusing on the environmental sphere of the sustainable development
principles.
This PhD project identified several critical gaps and deficiencies of the MinReF in WA where
a track record exists about developing mining legislation to support, and manage the mining
industry for over a century. This study identified seven weaknesses of the MinReF and
discussed in detail in Chapter Eight and summarised in Chapter Ten. The findings indicate
some strengths, but also the weaknesses of the MinReF. It is important to note that the current
gaps and deficiencies of the MinReF were identified not as problems, but as opportunities to
assure environmental protection as this study provide directions to address the weaknesses.
In response to the seven key findings. Further, this study, proposed a series of
recommendations to address current gaps and reduce duplication of agency functions and
proposed an adaptive capacity for the improvement of the MinReF of WA.
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11.2 Recommendations
This study included a research objective to “propose ways and means of improving the
Western Australian mining regulatory framework to assure environmental protection”. In line
with the research objective, this chapter proposes recommendations to help achieve and
address current gaps and deficiencies identified as an outcome of this research. One critical
recommendation is to establish an apex-level agency to coordinate all resource development
activities by adopting a whole-of-government strategy. Another proposal is to develop a
resource development policy, as the State of Western Australia is yet to establish a well-
coordinated approach to manage century-old mining operations. It is essential that any future
changes to MinReF must be focused on the existing strengths without compromising them
but, also exploring opportunities to address the current weaknesses which will position mining
as a sector within the sustainable development concept and its principles as practicable as
possible.
The recommendations put forward in this thesis (Table 11.1) are aimed to achieve this goal
and address the fourth research objective of this study.
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TABLE 11.1 RECOMMENDATIONS TO ADDRESS GAPS AND
DEFICIENCIES OF MINING REGULATORY FRAMEWORK
ISSUE RECOMMENDATIONS (R)
At present, there is no a whole-of- (R 1) Develop a whole of Government
government Resource Development Resource Development Policy
Policy for Western Australia despite
having mining regulations operating for
over 100 years.
At present, there is no whole-of- (R 2) Appoint an independent inquiry to
government policy on mine identify costs for developing mine
rehabilitation and closure plans for the closures plans for large resource projects
resource projects that operate under 64 operating under the State Agreements
State Agreements (and the ones that (SAs).
have already been revoked).
(R 3) Explore measures to collect mine
The current mine rehabilitation rehabilitation levies by making
legislation (MRF Act) is inadequate and amendments to the MRF Act to collect a
does not cover the larger mines and regular levy (to be determined in
resource projects regulated under the consultation with mining companies that
State Agreements. operate under SAs)
This dichotomy and ambivalence of (R 4) Assess environmental, economic
mining legislation need to be addressed and social risks associated with difficult to
by proposing legislative solutions after rehabilitate abandoned mine sites that
a formal independent review of the could harm people and animals.
current regulatory framework and
ensure current legislative gaps are (R 5) Explore and implement innovative
identified and remedied. mine rehabilitation programs including
involving community groups to carry out
mine rehabilitation work based on the
global and Australian best practice
examples.
There have been no regular formal (R 6) Undertake an inquiry into the current
evaluations of the efficiency of State state of operations and management of
SAs.
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Agreements (SAs) since this regulatory The inquiry should include the validity of
mechanism was established in 1952. some of the old SAs such as the Act
which is still used to manage the Yeelirrie
The WA Auditor General conducted an uranium mine as in this study established
audit into the status of SAs in 2004. evidence that the Yeelirrie (Uranium) Mine
However, the bulk of the findings have Act 1978 may not be valid.
not been followed up.
This research study found: (R 7) Explore the feasibility of setting up a
(i) inherent weaknesses of key Resource development and management
mining legislation; (ii) unclear division (apex-level entity) preferably
demarcations and overlaps of under the Premier and Cabinet.
legislation; (iii) ambivalence and
dichotomy of the mining regulatory Most of the resources required could be
framework; (iv) lack of coordination of secured by streamlining and restructuring
mining regulatory framework and multi- the functions DMIRS & DJTSI.
agency roles; (v) absence of an apex-
level agency to coordinate mining
regulations; (vi) delays in introducing
environmentally-centric legislation and
regulations, and (vii) lack of adaptive
capacity. Most of these findings could
be addressed by setting up an apex-
level agency preferably under the
Department of Premier and Cabinet to
coordinate, monitor and continuous
improvements of mining regulations in
WA.
11.3 Future Research Agenda
The focus of this PhD project was limited to the findings that emerged from an in-depth
examination of the Mining Regulatory Framework in Western Australia, and an evaluation of
relevant regulations of two types of mining approval and operations through case study
method. The PhD project was limited to examine the efficiency of the environmental
compliance of the mining regulations in WA focusing on two minerals—uranium and coal.
Several other research topics were not covered in this study (see Table 11.2), hence they
need to be studied focusing on other aspects of the mining regulatory framework of WA. The
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APPENDIX A INFORMATION SHEET FOR PARTICIPANTS
Date: 14 October 2016
INFORMATION SHEET
Information sheet for the research participants about the doctoral research project on
the Mining Regulatory Framework (MinReF) of Western Australia
My name is Sunil Govinnage, and I am currently undertaking research towards a PhD
degree at Curtin Sustainability Policy (CUSP). The title of my research project is
“Environmental regulations of the mining industry: Two case studies from Western Australia”.
My research focuses on the primary research question to explore: “How is the mining
regulatory framework in Western Australia being implemented legislatively environmental
protection during the mining life cycle?” My research will focus on two case studies. The
first case study examines the environmental compliance and consequences of coal mines
located in the Collie region in south-west Australia. The second case study will examine the
regulatory framework consisting of the State and Federal legislation, employed to grant the
approval of the environmental compliance as a prerequisite of mine operation.
I would like to find out about your opinions, views and perceptions on the WA’s mining
legislation in general, and the implementation of environmental protection regulations
specifically, based on your work experience and/or research publications on this subject.
This proposed semi-structured interview will take approximately 45 – 60 minutes. All the
questions will be read out to you, and your answers will be recorded during the interview. In
the analysis of data, your name or position will be not used or revealed, and the interviewee
will always remain anonymous.
Consent: Your involvement in this research is entirely voluntary.
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You will be given the opportunity to see the questions beforehand and decide whether you
would like to participate in the interview. When you have ticked the AGREE box on the
consent form, I will assume that you have agreed to participate in my research and allow me
to use the information provided for this particular research. However, you have the right to
withdraw at any stage of the interview process without having to give me a reason.
Confidentiality: The interview is anonymous, and your privacy is greatly respected; no
personal information will be obtained or required for this research. The results from the
interview will be presented only as the general discussion in my thesis, either to validate or
further examine issues identified for the purpose of this research. The information collected
will be used only for this particular research. In adherence to the university data
management policy, the information gathered from this proposed interview will be kept as a
typed-transcript in a secured server as per university data management policy, and after
seven years the transcripts will be destroyed.
Further information: This research has been peer-reviewed and received the approval of the
Human Research Ethics Committee of the Curtin University. (Approval number RDHU-89-
15).
If you would like further information about my research, please feel free to contact me on
04322 47330 or by email: [email protected]. Alternatively, you can
contact my principal supervisor Professor Dora Marinova on 08 9266 9033 or via email:
[email protected].
Thank you very much for your involvement in this research project, and your participation is
very much appreciated.
Sunil K Govinnage (M.A. Science & Technology Policy, Murdoch)
PhD Candidate
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APPENDIX B QUESTIONNAIRE
Thank you very much for granting time for an interview despite your busy schedule.
I’m Sunil Govinnage interviewing ======== in Perth on ====
First, I want to have your consent for this interview to be recorded and that I have provided
you with an information sheet prepared for the participants of this research
Any information, you may provide will remain anonymous, and any issues that you will share
with me for the purpose of my PhD research will not be associated with your name, position
or the agency you are affiliated with.
I may use some of the information as qualitative statements in my thesis.
I want to begin the interview by asking your opinion of the term ‘environmental protection’
based on the WA Environmental Protection Act 1986 on page 1
The term ‘environmental protection’ is used to denote "the prevention, control and
abatement of pollution and environmental harm, for the conservation, preservation,
protection, enhancement and management of the environment and for matters incidental to
or connected” (Government of Western Australia, 1986, p.17).
(1) In your view, is this a good working definition to cover core mining environmental
regulations?
Do you have any comments?
(2) As you are aware, the mining industry needs a large quantity of water for mining
operations. What is your opinion about the omission of water in this definition and, in
particular, the lack of references to the prevention of ground water and nearby water
resources (creeks, rivers, and reservoirs). Please elaborate your reasons?
(3) As you are aware, the current Mining Regulatory Framework (MinReF) could be broadly
defined as State and Federal laws consisting of numerous policies, procedures and
administrative tools managed by several existing agencies to regulate and manage the
mining industry in WA.
(4) In your view, what are the strengths and weaknesses of the current MinReF as
implemented in Western Australia?
Follow up question/s:
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5.1 Please explain your reasons or provide examples of particular strengths of the MinReF;
5.2 Please explain your reason/s or provide examples of specific weaknesses of the
MinReF.
5.3 What are your thoughts about the following opinion on the WA mining regulations
regarding environmental impact? (Give a hard copy version of the following statement to the
interviewee)
“WA legislation provides a strong and comprehensive basis for regulating the
environmental impacts of mining. But legislation alone cannot guarantee an effective
regulatory regime.”
Chandler, L. (2014). Regulating the Resource Juggernaut. In Brueckner, et al (eds.)
Resource Curse or Cure: On the Sustainability of Development in Western Australia.
pp. 165-178, Berlin: Springer Verlag
MINNING OPERATIONS
(6) In your opinion, are there appropriate checks and balances to ensure environmental
protection during mine operations in WA? Please elaborate/expand including listing and
describing some of the appropriate/relevant checks and balances.
ENVIRONMENTAL BEST PRACTICES
(7) Could you please discuss any national or international environmental best practices that
you are aware of concerning approval, operation and/or closure of mines (either in Australia
or elsewhere)? Please provide any information or references that you are aware of in
academic writings on mining literature.
ON STATE AGREEMENTS
As you are aware, the State Agreements are “contracts between the Government of Western
Australia and proponents of major resources projects.” (Department of State Development
n.d.). They outline the terms and conditions stipulating the rights, obligations when
developing a particular resource project. Once the proponent and the responsible agency
have agreed to the terms of the contract, they will be ratified by the Parliament.
These Agreements function above the existing laws of the State and operate outside the
jurisdictions of the WA Mining Act 1978, which is supposed to be the principal legislation
regulating the Mining Industry in WA. The State agreements have an operational history of
over 50 years in WA. They have been reviewed only once, in 2004, by the Auditor General
of Western Australia examining their operational effectiveness.
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(8) What is your opinion on approving long-term resource agreements which operate
above/outside existing laws of the State without any public consultations, and ratifying them
in the Parliament giving the authority to operate?
(9) In the context of public policy development processes, what are the strengths and
weaknesses of the WA State Agreements? Please elaborate your reasons.
The literature reveals that Queensland is no longer adopting the long-term State Agreements
to initiate and operate resource development projects where all the mining regulations are
carried out through existing legislation.
(10) Do you think that WA should follow the practice of Queensland? If so, why?
(11) Do you have any thoughts/suggestions on improving the current processes of State
Agreements with emphasis on improving the environmental regulations of the mining
industry?
ON URANIUM MINING
When the Barnett government came to power in 2008, the moratorium on uranium mining
was removed, and the government gave directions for the approval of uranium mines in WA.
As of April 2015, two uranium mines have received the environmental approval. process. A
literature review suggests that lessons learnt from the uranium mining in the Northern
Territory and South Australia have not been incorporated into the regulations of uranium
mining in WA.
(12) In your view, what are the key lessons on environmental protection that WA could learn
from the past uranium mining in the Northern Territory and South Australia?
POLICY RELATED QUESTIONS
The literature review on this research reveals the WA MinReF is being implemented through
a multi-agency approach and regulations have not been properly followed through by
responsible agencies, and that there are critical gaps in the current approach. For example,
the WA Auditor General’s report titled Ensuring Compliance with Conditions on Mining tabled
in the Parliament in 2011 states:
“Monitoring and enforcement of environmental conditions need significant improvement.
Currently [all] agencies can provide a little assurance that the conditions are being met.
Further, the Report reveals:
“Only 55 percent of sampled operators submitted their required Annual Environmental
Reports (AERs) to DMP providing regular information on whether they are minimising their
impact on the environment.” (p.8).
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As far as the information gathered from literature reviews suggests, this crucial issue has not
been addressed through the ongoing mining regulatory reform process initiated by the
Government of Western Australia through the Dept. of Mines and Petroleum (DMP).
(13) Why do you think that this key gap has not been addressed to date?
(14) What is your opinion on not addressing a key gap (deficiency in reporting) essential for
monitoring and managing environmental conditions of mining?
The follow up question:
(15) `Why do you think there has been a delay in addressing environmental compliance
reporting shortcomings? Please elaborate.
The Environment Protection and Biodiversity Conservation Act 1999
As you know The Environment Protection and Biodiversity Conservation Act 1999 (EPBC
Act) “is the Australian Government’s central piece of environmental legislation.
However, according to a bi-lateral agreement between the Federal and the State of WA
which came into effect on 1 January 2015, the EPBC Act’s authority to assess proposals that
are likely to have a significant impact on national environmental significance will be now
carried out by the WA Environmental Protection Agency.
(16）In your view, has the change of authority, through delegation of the Federal
Government’s responsibility to the State, enhanced or decreased the effectiveness and or of
EPA assessments of proposals that are likely to have a significant impact on national
environmental significance?
(17) Why do you think this delegation has occurred and has this delegation weakened or
strengthened the intention/purpose of the legislation?
Thank you very much for your time today.
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APPENDIX C THE FEDERAL GOVERNMENT’S RESPONSE TO THE
NATIONAL AUDIT REPORT ON THE EPBC ACT
Parliament House, Canberra ACT 2600Telephone (02) 6277 7920
[email protected]
AUSTRALIA
The Hon Greg Hunt MP
Minister for the Environment
16-004235
Mr Sunil Govinnage - 7 MAY 2016
vinnage,
Dear Mr C---«-4
I refer to your letter of 2 April 2016 to the Prime Minister, the Hon Malcolm Turnbull MP,
concerning implementation of recommendations from a Performance Audit titled Managing
Compliance with the Environment Protection and Biodiversity Conservation Act 1999. The
Prime Minister has referred your letter to me for reply.
In response to the questions posed in your letter, the Department of the Environment
(the Department) has implemented a number of measures to meet the recommendations of the
Performance Audit. These include:
•
A new Compliance Monitoring Program based on risk.
•
A risk prioritisation tool, developed in collaboration with the Commonwealth Scientific and
Industrial Research Organisation (CSIRO). The tool enables the Department to focus its efforts
towards those approvals that pose the greatest potential risk to matters of national
environmental significance.
•
Standardisation of business practices and upgrades to IT systems. More than 60 standard
operating procedures are now in place to support compliance monitoring activities. Enhanced
IT systems have also improved the Department's monitoring, compliance and intelligence
capabilities.
•
A quality assurance framework to ensure performance benchmarking, review and continual
improvements to compliance monitoring activities.
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ABSTRACT
Open-pit mines, especially open-pit mining complexes, are a kind of
large-scale, integrated, and complicated operating system, which requires
significant initial capital cost and sustaining capital cost. A successful
mining operator knows how to maximise benefits from mine development
via good strategic mine planning. Open-pit mine production scheduling
(OPMPS) involves strategic decision-making that seeks to optimise the
mining sequence and the materials flow (i.e. processing streams,
stockpiles, waste dumps) within given constraints. The space availability
typically is a common constraint during the mining layout study. However,
the strategic mine planning for those open-pit mining complex by
manually has great difficulty. Meanwhile, the available commercial
mining software is unable to be developed by being tailored for those
specific open-pit mine scheduling problems.
The research work aims to solve the production scheduling problem for
open-pit mining complexes. It establishes a Mixed-Integer Programming
(MIP) model that maximises the net present value of future cash flows and
satisfies reserve, production capacity, mining block precedence, waste
disposal, stockpiling, and pit sequence constraints. The model is validated
by using small to medium scale datasets. All formulated constraints have
worked correctly based on the validation results.
It is presented using a real data set from a gold mine in Western Australia
to test a proposed MIP model. The case study is based on the given mining
physicals, which assesses the mine strategy plan of the open-pit mining
complex by conjunction with the simultaneous optimisation of extraction
sequence and processing stream decisions. On the basis of the same
dataset, two scenarios are examined, which indicates that the proposed
MIP model can generate a mine schedule to fit the constraint of limited
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CHAPTER 1. INTRODUCTION
Surface mining technique, namely open-pit mining or open-cast mining,
is a mining method that the rock or minerals are extracted from the earth.
As a widely used mineral extraction method, Open-pit mining is chosen
when minerals or deposits are found relatively close to the surface.
Usually, two or more open-pit mines, processing flows, stocks, mixed
options, and products are composed of an open-pit mining complex.
Optimising the mining complex scheduling is designed to maximise the
net present value (NPV) of cash flow by generating a production plan for
the entire mining activity (Goodfellow and Dimitrakopoulos 2016) .
The open-pit mine production scheduling (OPMPS) problem consists of
(i) identifying a mineralised zone through exploration with drilling and
mapping,
(ii) dividing the field into three-dimensional rectangular blocks, and
creating a block model to represent the mineral deposit numerically,
(iii) assigning attributes such as grades that are estimated by sampling
analysing drill cores, and
(iv) utilising the attributes to evaluate the economic value of each block,
i.e., differences between the expected revenue from selling ore and
associated costs such as those related to mining and processing. Given this
data, the further work's target is to maximise the mine project’s NPV by
determining each block's extraction time in a deposit and confirm the
destinations of which the blocks must be sent to the processing streams,
stockpiles, or waste dumps.
The quantity and quality of production will be determined, reaching
millions of dollars over the life-of-mine (LOM). An optimal sequence for
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annually extracting the mineralised material is determined by the annual
production scheduling of an open-pit mine.
Figure 1.1 describes a typical open-pit mine design process. The process
starts with the assumption of initial production capacities and estimates
for the related costs and commodity prices. Once the economic parameters
are known, the analysis of the ultimate pit limits of the mine is undertaken
to determine what portion of the deposit can economically be mined. The
ultimate pit shell divides the entire deposit into two subgroups. First, ore
reserves is the minable ore within the ultimate pit shell. This is usually
done by using the moving cone method or the method of Lerchs and
Grossmann (Lerchs 1965).
Figure 1.1 Steps of traditional planning by Circular Analysis (Dagdelen,
1985)
Within the ultimate pit limits, pushbacks are further designed to divide
deposit into nested pits, going from the smallest pit with the highest value
per tonne of ore to the largest pit with the lowest value per tonne of ore.
These pushbacks are designed with haul road access and act as a guide
during the scheduling of yearly productions from different benches. The
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1.1.2 Block Economic Value (BEV) and Discounted Cash Flow (DCF)
The purpose of open-pit production scheduling is to determine the LOM
plan under certain technical and operational constraints to maximise the
value of mine. This process involves calculating the net economic value
of a single block. According to the estimated economic value of blocks,
the optimal solver chooses each block's optimal destination under the
given technical constraints to maximise the total pit value. Many
researchers have studied the economic value equation of blocks, such as
Ataee-pour (Ataee-pour 2005), and Whittle (Whittle and Wooller 1999).
The BEV calculation formula is defined as the revenue from selling
recovered metal at a specific fixed metal price, minus pit extraction cost,
ore processing cost, and other applicable costs. Economic value is then
assigned to a single block. The Whittle’s BEV equation is the following
(Whittle and Wooller 1999)
BEV = T GRP− T C − TC Equation 1
o o p m
where:
𝐵𝐸𝑉 block economic value, $,
𝑇 ore tonnage of the block,
𝑜
𝐺 ore grade, unit/tonne,
𝑅 metal recovery rate,
𝑃 unit metal price, $/unit,
𝐶 the unit cost of processing, $/tonne,
𝑝
𝑇 rock tonnage of the block,
𝐶 the unit cost of mining, $/tonne.
𝑚
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DCF analysis is used in the process of strategic mine planning (Whittle
2000). It is convenient to consider the pit optimiser as an engine within
the planning process that partly answers the first question by finding the
pit design that maximises the difference between variable costs and
revenues.
In simple cash flow analysis, the question of “whether the project should
be proceed or not” is answered in the affirmative if the calculated value is
greater than the cost of capital.
DCF analysis adds to this the concept of cash flow discounting.
Discounting determines the present value of a future payment or stream of
payments, which is performed to remove the capital cost and remove the
relevant cost from a particular project. The resultant value of the
calculation is the project NPV. This means the project's value is in excess
of that is required to pay the cost of capital and compensate for the risk
associated with the project. The answer to the second question posed at
the beginning of this section is answered if the NPV is positive.
The rules that govern which costs should be included can be stated simply
(Whittle 2000):
● All costs which vary according to the amount of waste, ore, or
product that is removed, processed, or sold should be included in
the pit optimisation model, and any costs which do not so vary
should not be included.
● All expenditure that was not included in the pit optimisation model,
except for the portion in spending that has already been committed
and is irreversible, should be included in the project evaluation
calculations.
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1.1.3 Ultimate Pit Limit Design
Two principal classical methods are widely used to determine the shape
of a surface mine. The first one is the floating cone method (Laurich and
Kennedy 1990), which assumes a block as a reference point for expanding
the pit upward according to pit slope rules. This upward expansion, which
contains all blocks whose removal is necessary for the removal of the
reference block’s removal, forms a cone whose economic value we can
compute. One can then take a second reference block and add to the value
of the cone the incremental value associated with the removal of the
additional blocks necessary to remove the second reference block; the
process then continues. Problems with this method include the following:
(1) the final pit design relies on the sequence in which reference blocks
are chosen, and (2) many reference blocks might need to be chosen (and
the associated value of the cone computed) to achieve a reasonable,
although not even necessarily optimal, pit design. Although the floating
cone method is used widely in practice, the seminal work of Lerchs and
Grossmann (Lerchs 1965), who provide an exact and computationally
tractable method for open-pit design. This problem can be cast as an
integer program (Hochbaum and Chen 2000), as described below.
(𝑏,𝑏′) ∈ 𝐵:Set of Precedences between blocks
𝜈 : value obtained from extracting block b
𝑏
𝑦 : 1 if block b is extracted, i.e., if the block is part of the ultimate pit, 0
𝑏
otherwise (variable).
Equation 2
𝑚𝑎𝑥∑𝜈 𝑦
𝑏 𝑏
𝑏
Subject to
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𝑦 ≤ 𝑦 ∀(𝑏,𝑏′) ∈ 𝐵 Equation 3
𝑏 𝑏′
0≤ 𝑦 ≤ 1 Equation 4
𝑏
1.1.4 Precedence relations
The precedence relationships between blocks geometrically constitute the
principal structural constraint geometrically in open-pit mine planning.
Subject to the “slope angles”, block i cannot be mined before a group of
the determined blocks that are “above” block i are removed.
As shown in Figure 1.3, two scenarios of block precedence relationships
are depicted. (i): if going to extract block 6, the five blocks above block 6
should be mined out; or, (ii): the nine blocks above block 10 should be
mined out prior to extracting block 10. The blocks “above” block 10
include the blocks one level higher and the front, left, right, back, or
diagonal with respect to a given block (Espinoza, Goycoolea et al. 2013).
Figure 1.3 two kinds of block precedence relationships. (i): if going to
extract block 6, the five blocks above must be extracted; or, (ii): the nine
blocks above block 10 must be mined prior to removing block 10.
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Equation 5
𝑚𝑎𝑥 ∑∑𝑦 𝐶
𝑏𝑡 𝑏𝑡
𝑏∈𝐵 𝑡∈𝑇
Constraints:
Equation 6
∑𝑦 ≤ 1 ∀𝑏 ∈ 𝐵
𝑏𝑡
𝑡∈𝑇
Equation 7
𝑀𝑙 ≤ ∑𝑚 𝑦 ≤ 𝑀𝑢 ∀𝑡 ∈ 𝑇
𝑡 𝑏 𝑏𝑡 𝑡
𝑏∈𝐵
𝑡 Equation 8
𝑦 ≤ ∑𝑦 ∀𝑏 ∈ 𝐵,∀𝑏′ ∈ 𝐵 ,𝑡 ∈ 𝑇
𝑏𝑡 𝑏′𝜏 𝑏
𝜏=1
𝑦 𝑏𝑖𝑛𝑎𝑟𝑦 ∀ 𝑏 ∈ 𝐵,𝑡 ∈ 𝑇 Equation 9
𝑏𝑡
Constraint (Eq.6) ensure that a block can only be extracted one time.
Constraint (Eq.7) limits the number of blocks removed during each period.
Constraint (Eq.8) ensures that a precedence constraint is validated.
1.2 Problem statement
A gold deposit features low-grade but large-tonnage, located in Western
Australia. The gold project consists of several open-pit mines that form an
open-pit mining complex. The open-pit mines were previously mined and
are scattered across the leases along the north-south direction. In the past,
the mined ore was hauled and treated in a carbon in leach (CIL) plant with
the capacity of 3.7 million tonnes per annum (mtpa), about 40 km away
from the north of the mine site. It is hard to continue to mine and treat the
remanent low-grade gold ore in the CIL plant economically. Considering
that heap leaching is a cost-effective technology very suitable for
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processing low-grade ores (Petersen 2016), the potential for a heap leach
project on the mine site is to be evaluated.
There are two main constraints on the mining complex. One is the
scattered pits. All mined ores from scattered pits need to be hauled to a
heap leach plant for centralised treatment adjacent to Pit 2. Another one is
the limited land space. The mining tenement features bell-shaped with
narrow side wings where the limited availability of land space is a
significant constraint on the layout of waste/ore stockpiles and heap leach
facilities. In the initial layout study, the waste dump is located in a large
lake district to the south of pits. It significantly increases the haulage cost
of waste rock and is detrimental to the heap leach project.
Considering the low content of metal sulfide minerals in the deposit and
no underground mining potential, an approach is dumping waste rock to
that mined-out pit and mined-out areas of active pits, which could alleviate
the tightened land use requirement, but challenge the production
scheduling with the synergism problem of mining production and waste
rock dump.
Figure 1.4 shows a schematic view of an open-pit mine production
scheduling problem with multiple movement destinations of materials.
After mining out a designated pit within the mining complex, the mined-
out pit can be utilised as an in-pit waste disposal facility and a waste dump
on top of the back-filled pit. This option provides a short-haul distance of
the waste rock and sufficient storage capacity for waste rock dumping over
the project's life of mine.
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1.4 Research Methodology
(1) Develop the MIP model first.
(2) Create the MIP model in CPLEX.
(3) Validate the proposed model using subsets of data with a small-scale
block model.
(4) Implement a model using a real-world dataset.
1.5 Significance
Based on an actual case, the research project gives a new model to solve
the mining production schedule for an open-pit mining complex.
The proposed mathematical models will generate a detailed production
schedule to achieve different objectives.
The approach uses mathematical programming to solve the particular
project's scheduling problem. This demonstrated optimality method is
tailored for an individual project, which is more accurate and catering to
mine owner's requirements, such as space limitation, gold-producing
priority, rather than the scheduling manually by commercial mining
software. The process of mathematical modelling is adaptable for
adjustments, which will benefit other similar scheduling problems in the
mining industry.
1.6 Outline of chapters
The thesis is organised as follows:
Chapter 1 focuses on the introduction of the thesis. The background, the
definition of the problem, and research objectives are presented.
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● Implement the solution to improve the system.
Blum and Leiss (2007) have framed mathematical modelling as a process
consisting of subsequent activities. It is usually necessary to iterate the
mathematical modelling cycle many times, as shown in Figure 2.1, in
order to obtain the optimal representation of problems.
2.2 MIP Model
Linear programming (LP) method is a popular mathematical model for
resolving optimization problems. As shown in equations 10 to 12, the
generalised LP model is composed of a linear objective function, some
linear constraints, and a set of non-negative restrictions (Topal 2003).
Maximise (or minimise) 𝑧 = 𝑐 𝑥 + 𝑐 𝑥 + 𝑐 𝑥 ··· +𝑐 𝑥
1 1 1 1 1 1 𝑗 𝑖
Equation 10
𝑎 𝑥 + 𝑎 𝑥 + ⋯ 𝑎 𝑥 ≤ 𝑏 Equation 11
11 1 12 2 1𝑛 𝑖 1
𝑎 𝑥 +𝑎 𝑥 + ⋯ 𝑎 𝑥 ≤𝑏
{ 21 1 22 2 2𝑛 𝑖 2 }
⋮ ⋮ ⋮ ⋮
𝑎 𝑥 + 𝑎 𝑥 + ⋯ 𝑎 𝑥 ≤ 𝑏
𝑚1 1 𝑚2 2 𝑚𝑛 𝑖 𝑚
𝑥 𝑥 ⋯𝑥 ≥ 0 Equation 12
1 2 𝑖
This objective z (Eq.10) corresponds to the value of interest, which is
equal to a function of the decision variables 𝑥 with the corresponding
𝑖
coefficients 𝑐. The Z value may stand for the cost or NPV, depending on
the formulation. It provides a numerical indicator to compare the solutions.
The limiting conditions of the problem are formulated in the constraint
sets (Eq.11), and the constant 𝑎 and 𝑏 are derived from the problem.
𝑚𝑛 𝑚
Furthermore, constraint (Eq. 12) restricts the values of 𝑥 .
𝑖
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It is possible to satisfy the constraints (Eq.11) and (Eq.12) of the LP
problem with many different solutions. But only one of those sets of
solutions can reach the maximum (or minimum) Z value. Depending on
whether maximization or minimisation is desired, this solution set is
defined as the optimal solution, which is mathematically proven.
A MIP is a form of LP that restricts some variables to integers and others
to continuous values. An integer variable can also be of a binary type. MIP
specifies various logical conditions in a binary variable, so the
mathematical model can solve the problem more accurately by specifying
some logical conditions(Li 2014).
2.3 Solution of MIP Model
After the mathematical model has been constructed, a problem needs to
be solved in order to determine the optimum approach. In the past, solving
simple LP problems with a graphical method (as shown in Figure 2.2) has
been accomplished by following the steps:
Step 1: Formulate the LP problem.
Step 2: Draw the constraint lines on the graph.
Step 3: Determine which constraint line is valid for each situation.
Step 4: Determine the feasible region.
Step 5: Create the objective function on the graph.
Step 6: Determine the optimum point.
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Figure 2.2 Illustration of the graphical method concept
The linear constraints outline the feasible region, where any points (X1,
X2) within this region satisfy the condition. The Objective function Z is
graphed and the value is calculated. An optimum solution set (X1, X2)
can be determined when Z value reaches the maximum or minimum,
depending on the optimisation nature of the problem. However, the
graphical method becomes impractical when solving problems with many
variables and constraints. In the late 1940’s, the simplex algorithm was
developed by Dantzig for solving more complicated linear programming
problems (Fourer, Gay et al. 1990). This method provides a standard
approach to solve any linear programming problems. It first converts a
problem into standard form. Then the problem is reconstructed to a table
form. The derivation of the optimum solution is via a series of row
operations on the table. The detailed solving steps are discussed by Taha
(2007). With the advancement of computing technology, computerised
row operation enables faster and accurate results generation. However,
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recognized in the mathematical sciences community for modelling and
finding optimal solutions for large, complex, and highly constrained
problems. MILP problems use linear objective functions, which are
constrained by linear constraints, to perform minimisation and
maximisation of the problem.
MIP has been used in mine planning for cut-off grade optimization,
equipment allocation, ore blending, stockpiles, and process stream
selection. Most of the studies on mine plans involved selecting blocks to
maximize NPV values.
To maximize the project NPV, the scheduling approach prioritizes
processing the highest value ore available in the early periods of mining,
subject to multiple considerations, such as mill throughput, mining
capacity, rock type, ore properties, and waste management.
2.4 MIP models application in the mining industry
MIP technique has been implemented into mining industry for more than
60 years. Many studies are available to provide MIP application and other
operations research techniques to optimize various aspects of both open-
pit and underground mining operations (Newman and Kuchta 2007,
Dimitrakopoulos and Ramazan 2008, Epstein, Goic et al. 2012). Most of
the researches on mine scheduling consists in selecting blocks to
maximize NPV value.
Mine production scheduling involves the sequence and timing of ore and
waste movement during the life of a mine or a complex. It determines the
destinations where the block is moving to, such as processing plant, ore
stockpile, waste dump, mined-out area of the active pit, and mined-out pit.
Various mathematical formulations have been developed to solve the mine
scheduling problems.
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Hoerger (Hoerger 1999) establish a MIP model to solve the scheduling
problem of multiple pits' simultaneous mining and ore delivery to multiple
plants. The model group blocks into increments and accounts for multiple
stockpiles. The model is successfully implemented at Newmont's Nevada
operations, where fifty sources, sixty destinations, and eight stockpiles are
present. The given solution will increase the NPV of operations if verified.
Caccetta and Hill (Caccetta and Hill 2003) developed a MIP model with
an objective to maximise the Project NPV over the sequenced blocks,
which added constraints including extraction sequence, mining, milling,
refining capacities, grades of the mill and concentrate, stockpiles, and
operational conditions such as pit bottom width and depth limit.
Stone et al. (Stone, Froyland et al. 2018) present the Blasor optimization
tool, which addresses using solver ILOG CPLEX to determine the best
extraction sequence for multiple pits as MIP.
Wooller (Wooller 2007) introduced Comet software that uses an iterative
algorithm to define operational strategies and process routes, such as heap
leaching versus concentration, to optimize the plant's yield/recovery rate
and cut-off grade.
Zuckerberg (Zuckerberg, Stone et al. 2007) optimized the extraction
sequence of bauxite "pods" from the Boddington bauxite mine in south-
west Australia. The pod is a distinctive body of medium sized ore located
near the surface.
Chanda (Chanda 2007) formulates the delivery of materials from different
deposits to metallurgical plants as a network linear programming
optimization problem. The model uses a network that includes mines,
concentrators, smelters, refineries, and market areas to minimize the costs.
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It is suggested that the scale of practical problems makes it difficult to use
the integer programming model for mine production. Therefore, it adds
heuristics and aggregation techniques to reduce the problem's size. This
approach aims to use aggregation techniques to get a suboptimal solution
to reduce the number of variables and constraints.
Ramazan (Ramazan 2007) uses a Fundamental Tree algorithm (FT) based
on linear programming. This method could lead to aggregate material
blocks and reduce integer variables and constraints to form mixed integer
programming formulas.
Badiozamani et al. (Badiozamani and Askari-Nasab 2016) used the MIP
model to solve the scheduling problems of oil sands mining sequence and
tailings pulp management. In this project, two techniques are constructed,
and the problem's size was reduced. In addition, this also makes the real
cases more valuable and practical.
Ramazan (Ramazan, Dagdelen et al. 2005) regards that simultaneous
optimization is a practical and well-developed and suitable way to
optimize the mining complex because it can perform global optimization
under all constraints.
The application of MIP is regarded as a solution that can solve the
production scheduling problem of open-pit mines, especially in large
open-pit mines with many blocks, which requires too many variables to
deal with the problem of time arrangement problem. Currently, the only
common practice is reconstructing the mining blocks before scheduling
(Figure 2.2), which creates an aggregate that is a subset of blocks on the
same bench and in the same grade group. It is customarily postulated that
all blocks' properties should be identical in an aggregate. Thus, the same
aggregate blocks will be sent to the same destination at the identical
mining productivity (Smith and Wicks 2014, Van-Dunem 2016). In this
approach, the optimization problem size obviously reduces, which can
significantly save the computing time for solving optimization problems.
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S. Ramazan (Ramazan, Dagdelen et al. 2005) proposed a MIP method to
solve a multi-element large open-pit's production scheduling problem.
Figure 2.4 A many-to-one relationship between the resource blocks and
the grouped blocks used for production planning (Martin L. Smith, 2014)
Most of the previous practices and studies are studying mining scheduling
optimization under the in-pit dumping of waste rock. The study of in-pit
dumping was also addressed by Zuckerberg (Zuckerberg, Stone et al.
2007) and Adrien (2018). However, there is a number of mine operations
that consist of multiple mining operations, but little research has been
done to establish a MIP model for solving the mining scheduling problem
of multiple mines. The most widely used method for multiple mines with
complicated constraints is utilise the commercial software as well as Excel
by assigning specific constraints. However, this manual method relies
heavily on the people experience and skills, and more likely generates
different schedules if conducted by different operators.
2.5 Summary
Extensive studies and practices have demonstrated the significance of MIP
technology on solving specific scheduling problems with various
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The reserve constraints ensure that all blocks are extracted only once.
𝑻 𝑷 𝑺 𝑾
∑[∑𝑿 + ∑𝒀 + ∑ 𝒁 ] ≤ 𝟏; ∀𝒎𝒃
𝒃𝒎𝒑𝒕 𝒃𝒎𝒔𝒕 𝒃𝒎𝒘𝒕
𝒕=𝟏 𝒑=𝟏 𝒔=𝟏 𝒘=𝟏
Equation 14
Mining block extraction precedence constraints
Prior to extract block b, the immediate predecessor blocks must be
extracted.
[∑𝑃 𝑋 + ∑𝑆 𝑌 + ∑𝑊 𝑍 ] − [∑𝑡 [∑𝑃 𝑋 +
𝑝=1 𝑏𝑚𝑝𝑡 𝑠=1 𝑏𝑚𝑠𝑡 𝑤=1 𝑏𝑚𝑤𝑡 𝜏=1 𝑝=1 𝑏́𝑚𝑝𝑡
∑𝑆 𝑌 + ∑𝑊 𝑍 ]] ≤ 0; ∀𝑚𝑏𝑡,𝑏́ ∈ 𝜇
𝑠=1 𝑏́𝑚𝑠𝑡 𝑤=1 𝑏́𝑚𝑤𝑡 𝑏
Equation 15
Mining capacity constraints
There is extraction capacity upper limit in period t.
𝐵 𝑃 𝑆 𝑊
∑[∑𝑞 𝑋 + ∑𝑞 𝑌 + ∑ 𝑞 𝑍 ] ≤ 𝐽 ; ∀𝑚𝑡
𝑏𝑚 𝑏𝑚𝑝𝑡 𝑏𝑚 𝑏𝑚𝑠𝑡 𝑏𝑚 𝑏𝑚𝑤𝑡 𝑡
𝑏=1 𝑝=1 𝑠=1 𝑤=1
Equation 16
Processing capacity constraints
The heap leach plant's ore processing capacity in period t is constrained.
𝑀 𝐵 𝑆
∑ ∑𝑞 𝑋 + ∑𝐸 ≤ 𝐾 ; ∀𝑝𝑡
𝑏𝑚 𝑏𝑚𝑝𝑡 𝑠𝑝𝑡 𝑡
𝑚=1𝑏=1 𝑠=1
Equation 17
Stockpile constraints
Equation 18 and Equation19 show the balancing equation for stockpiles'
inventory through t periods. Inventory of stockpiles at the end of period t
is equal to the calculated result from the amount of incoming materials at
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period t plus the amount of inventory at the end of t-1 minus the amount
of outbound at period t. The upper limit of stockpile storage capacity is
constrained in period t (Eq.20).
𝑀 𝐵 𝑃 Equation 18
𝐸 + ∑ ∑𝑋 − ∑𝐸 − 𝐸 = 0;∀𝑠,𝑡 ≥ 2
𝑠(𝑡−1) 𝑏𝑚𝑠𝑡 𝑠𝑝𝑡 𝑠𝑡
𝑚=1𝑏=1 𝑝=1
𝑀 𝐵 𝑃 Equation 19
∑ ∑𝑞 𝑋 − ∑𝐸 − 𝐸 = 0; ∀𝑠,𝑡 = 1
𝑏𝑚 𝑏𝑚𝑠𝑡 𝑠𝑝𝑡 𝑠𝑡
𝑚=1𝑏=1 𝑝=1
𝑆 Equation 20
∑𝐸 ≤ 𝐿 ; ∀𝑡
𝑠𝑡 𝑡
𝑠=1
3.2 MIP Model Verification
The proposed MIP model is programmed in the OPL code of IBM ILOG
CPLEX Optimization Studio (Version 12.10). The optimality gap is set to
0.01%. To verify the MI
P model, the model is tested with four datasets.
3.2.1 Input Data Set
A mining complex including three open-pit mines is employed for this
verification. In datasets, 600, 1,500, 3,000, and 4,500 mining blocks in
total are assumed to be mined. All mines of each dataset have the same
number of blocks. Each mining block is initially assigned with attributes,
such as block coordinates, ore grade, density, etc. Each block is also
assigned with a block ID, making each block unique and validating block
movement destination in the schedule.
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3.2.2 Problem Size and Solution Time
The optimum solution is determined by CPLEX optimizer, which runs on
a computer with 256 GB NVM.2 hard drive, 8×2.9 GHz processors, and
48GB of RAM, operating under the Windows 10 environment.
Table 3.1 Problem sizes and solving time
No. of Binary CPU
Periods(a) Constraints
blocks variables time(s)
Dataset-1 600 6 37,038 21,600 9
Dataset-2 1,500 6 93,222 54,000 30
Dataset-3 3,000 6 219,216 108,000 68
Dataset-4 4,500 6 369,198 162,000 8,100
As shown in table 1, as the number of blocks increases from 600 to 4,500,
the problems will be amplified and the computing time soar from 9 second
to 8,100 seconds.
3.2.3 Implementation Results
With the implementation of four sets of data, the verification results reflect
that the optimum solutions satisfy the given constraints. It is ensured that
the designated mine is completed first. Secondly, the mining block's
extraction is restricted with the mining block precedence under the slope
angle constraint. Those constraints, such as the mining capacity, plant
capacity, and stockpile storage capacity, have been met. The highest-grade
ore is processed in the early stages to the greatest extent.
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CHAPTER 4. MIP MODEL IMPLEMENTATION
This section demonstrates the real-world implementation of the developed
MIP models. It includes an introduction to the mining project, MIP
problem solving, results in generation and analysis and mining sequence
scenarios.
4.1 Background
The project, located 10 km south-west of Kalgoorlie, Western Australia,
is divided into two parts, the north and south. Some infrastructures such
as highway, railway, and portable water pipeline are sitting in the middle.
This study case is focusing on the southern part of the project.
The open-pit mining complex includes several independent pits which
were previously mined and are scattered across the leases along the north-
south direction. The estimated resource within the leases is 2.7 Moz of
gold in total including Pit 1 (26.7mt @ 0.84g/t Au for 614 Koz), Pit 2
(16.2mt @ 0.95g/t Au for 493 Koz), and Pit 3 (26.8mt @ 0.96g/t Au for
826koz). In the past, the mined ore was hauled and treated in a carbon in
leach (CIL) plant with the capacity of 3.7 million tonnes per annum (mtpa),
approx. 40 km away from the mine site. It is hard to continue to mine and
treat the remanent low-grade resource in the CIL plant economically.
Considering that heap leach technology has a cost advantage in treating
low-grade ores, the potential to construct a heap leach plant on the mine
site has been evaluated technically and economically, and a leach plant
with a throughput of 6.5 million tonne per year will be built.
There are two main constraints on the open-pit mining complex. One is
the scattered pits. All mined ores from scattered pits need to be hauled to
a heap leach plant for centralized treatment adjacent to Pit 1, and
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minimizing the haulage distance of waste rock is a challenge to the mine
design. Another one is the limited land space. The mining tenement
features bell-shaped with narrow side wings where the limited availability
of land space is a significant constraint on the layout of waste/ore
stockpiles and heap leach facilities. In the initial layout study, the waste
dump is in a large lake district to the south of pits, which is hard to be
approved by the government. It significantly increases the haulage cost of
waste rock and detrimental to the heap leach project.
Figure 4.1 Mine site topography as mined
Considering the Non-Acid Forming (NAF) deposits of this project and no
underground potential, an proposed approach is dumping waste rock to
those mined-out pits, minimizing the waste haulage cost and alleviating
the tightly land use requirement but challenge the production scheduling
with the synergism problem of mining production and waste rock dump.
4.2 Geology
The prospect of this project is considered to be primarily composed of an
epiclastic sedimentary sequence and a suite of felsic porphyritic intrusions
that occur along a Fault. The regional metamorphic grade is lower to mid-
greenschist facies based on petrographic studies. Historically, the
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epiclastic sediments are considered to be conformable with the overlying
conglomerates of the Kurrawang Syncline.
Porphyritic intrusions can be distinguished into two groups based on
alteration; hematite altered, and sericite altered. The sericitic porphyry is
compositionally uniform, incorporating blocky white feldspar
phenocrysts in a glassy, sericitic pale green altered, groundmass.
Differentiation of the haematitic porphyry is based on the altered
groundmass, which is dark red. The feldspars, similar to the sericitic
porphyry, are blocky and white and the groundmass remains glassy. The
relationship between the groups has not been established. Numerous
porphyritic conglomerates or breccia aprons are present throughout the
tenement package, comprised of rounded clasts of porphyry, ranging in
size from centimetre scale to 0.5m in diameter. These flows are believed
to have formed by the over steeping of dome structures and are observed
to have an agglomeratic texture with a very fine grained glassy matrix.
Occasionally within the matrix are euhedral white feldspar phenocrysts,
as well as clasts of fine grained sandstones and siltstones. The silt-
mudstones are commonly laminated, compositionally uniform with a well
developed regional foliation. Inter-bedded silt and mud layers within the
sandstones occur commonly throughout the sedimentary sequence. The
dominant unit in this project area is a sequence of sandstones (arenites) of
varying grain size separated by siltstones. Typically the sequence is
graded, from fine grained to very coarse grained with well developed
bedding and cross-bedding. Soft sediment structures are observed
throughout, involving mainly dewatering flame structures and impacted
pebbles. The sandstone is generally dominated by rounded quartz with
minor amounts of feldspar and rock fragments. Pebble lags occur
occasionally within the series, although these intervals are discontinuous.
The thick to massive bedded sandstone is characterized by a lack of well
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developed sedimentary structures, a coarse to very coarse grain size, and
an immature and sub-arkosic composition.
4.3 Mine Design
The project concept involves using the existing Hitachi EX3600 excavator
and Cat 789 trucks to mine waste pre-strip, then joined by Hitachi EX2600
excavator and Cat 777 truck fleet to mine ore and waste.
The case study will be based on the given mining physicals. The mine
design reflects experience at the previously mined pits. A geotechnical
assessment was conducted for pit design purposes, but ongoing
geotechnical work will be required during operations. The proposed pits
will be up to 260 m deep at the Southern end, 4.5 km long, and 450 m
wide.
The overall slope varies from 42 degrees in the south end to 53 degrees in
the north. Batter angles vary from 40 degrees in oxide to 70 degrees in
fresh rock. Ore will generally be mined in 10 m benches. Figure 4.1 shows
the ultimate pit shells and the blocks with the final pits.
As the pit will be deepened to approximately 180m depth, sumps and pit
dewatering equipment will be required to dewater the pit. From the pit
sumps water will be nominally discharged to Pit 2. The pit dewatering
plumbing system will also deliver clear water to the Stormwater collection
ponds at the Heap Leach pad site where it can be used as make up water.
As shown in Figure 4.3 and Figure 4.4, additional or expanded waste
dump designs are required to accommodate approximately 149 million
tonnes of excavated waste during the ten year operation. Backfilling of Pit
2 allows the existing waste dumps to be expanded.
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of the mines. Regarding with the mining physicals generated by Whittle,
it has been partially adjusted in order to meet the production
4.7 Results and Analysis
4.7.1 Overview
Table 4.1 shows the MIP model implementation results of the project. The
results indicate that a reasonable NPV is estimated comparing to the
original project study based on the existing method in mining software.
The computing time is acceptable to the actual use.
Table 4.1 Summary of results
No. of Binary CPU
Periods(a) Constraints NPV
blocks variables time(s)
A$ 211.1
5,810 10 1,451,990 360,000 18,737
million
4.7.2 Results
As depicted in Figure 4.5, the pre-production stripping is done in year one
with low stripping volume because all open-pit mines are previous-mined.
The stripping ratio from year one to year three is continuously increased.
Between year 4 and year 8, there is a relatively stable mining production
with a strip ratio of 2.6 tonnes of waste per tonne ore.
Figure 4.6 shows the mine’s current strategy. Mine extraction of Pit 1 and
Pit 3 were launched after mine Pit 2 closed in year 3. Since from year 4,
the waste rock will be dumped to mine-out Pit 2. The ore mined is
relatively sufficient to meet the requirements of mill load, which facilitates
the balanced production with the stockpile.
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It can be observed from Figure 4.13 that the pre-tax NPV is 417.0 million
Australian dollars with a discount rate of 5%, and it drops gradually to
272.6 million Australian dollars with the discount rate increase to 10%.
Figure 4.13 Sensitivity analysis of discount rate
4.8 Mine Schedule without Pit Extraction Constraint
In order to deal with those components and decisions that have a
significant impact on the value of the project over the long term, a new
scenario without pit extraction constraint has also been studied. It assumes
that land space of the project is sufficient for waste dumping over the
LOM.
Without pit extraction constraints, working faces are available, thus
creating a more stable ore supply to the mill. As shown in Figure 4.14 and
Figure 4.15, three open-pit mines are operating over the life of mine. Only
in year 9 and year 10, the tonnage of mined materials begins to decrease.
Mill throughput is very stable from year 1 to year 9, and the feed grade
has a downward trend, indicating a good cash flow in the early stage in
Figure 4.16 and Figure 4.17. It is observed that the stockpile has more
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CHAPTER 5. CONCLUSIONS
5.1 Summary
The research work aims to solve the production scheduling problem for
open-pit mining complexes. It develops a MIP model that maximises the
net present value of future cash flows and satisfies reserve, production
capacity, mining block precedence, waste disposal, stockpiling, and pit
sequence constraints.
• The model is validated by using small to medium scale datasets.
The validation results have proved that all formulated constraints
are working correctly.
• The proposed MIP model is applied to a real data set from a gold
mine located in Western Australia. The case study is based on the
given mining physicals, which assesses the mine strategy plan of
the open-pit mining complex by conjunction with the simultaneous
optimisation of extraction sequence and processing stream
decisions.
• Two scenarios are studied using the same data set, which indicates
that the proposed MIP model can provide a practical mine schedule
to satisfy all given constraints. Compared to the original schedule,
the chosen schedule has less static income, million dollars.
However, the chosen schedule can come through the permitting one
and half years earlier, which brings a higher NPV through a 10-year
period of LOM.
• The established MIP model is flexible to adjust the given
constraints and decision variables, which can solve more
complicated problems of the mining industry.
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A
BSTRACT
In the last decades, mine planning and optimization is predominantly focused on either
open-pit or underground mining method only. It has neglected the other options as a
viable option in the early stage. This situation commonly happened in cases where
shallow deposits are mineralized to a considerable depth. These deposits are usually
planned using open-pit mining. Subsequently, underground mining strategy has emerged
as an option when the open-pit operation is approaching the ultimate pit limit. At this
point of time, the ‘transition problem’ arose in which a decision on either to extend the
pit or move to underground mining must be made. To solve this problem, it is suggested
that a mine optimization process which considers both open-pit and underground mining
be implemented simultaneously in order to generate economic benefits and provide a
clear guide to the decision-making process during the operation. From the review of the
current literature, it has revealed that there is a demand on methodology which can solve
the transition problem. Hence, the aim of this research is to develop a mathematical model
to solve the transition problem.
This research is focused to answer the question of ‘where and when to make the
transition’. To incorporate the practicality aspects in the combination of open-pit and
underground mining strategy, the framework of this research is to develop mathematical
models which consider not only open-pit mining and underground mining concurrently,
but also crown pillar placement. Two new mathematical models are developed. The first
proposed optimization model which aims to generate the optimal mining layout and
optimal transition point by maximizing the project value. This model has answered the
first part of the question (where to make the transition). The second optimization model
is developed to solve the transition problem by taking time-variant factors into account.
This model can provide the optimal transition point, transition period and crown pillar
location. Hence, it is possible to answer the questions of where and when simultaneously.
To solve the transition problem, the computation complexity is increased manifold
compared to a standalone optimization problem. Thus, the scale of the problem is a major
challenge in this research. Two main strategies to reduce the scale of the problem are
presented in this research. Firstly, a stope-based methodology is implemented for
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underground mining. This methodology is used to search and retain the profitable stopes
and eliminate those unprofitable stopes. The second strategy is an agglomerative
hierarchical clustering algorithm which is employed by open-pit mining. This strategy is
manipulated to cluster blocks within the ultimate pit by using a similarity index. A new
similarity index formula is proposed and employed in this research.
The proposed optimization models and hierarchical clustering algorithm are tested by
using two-dimensional datasets. The results are verified. The outputs of the models
proved that all the constraints that are designed for open-pit mining, underground mining
and crown pillar are correctly formulated and fulfilled.
The implementations of the proposed models are presented in this research. The
solutions confirm that the proposed models are capable to solve the transition problem
by maximizing the undiscounted or discounted cashflow. The Transition Point Model
achieves a maximized undiscounted cashflow of $3.74 billion and the Transition Period
Model attains $2.60 billion of net present value with no production delay while making
the transition from open-pit to underground mining. An additional scenario is completed
while considering two schedule period of production delay during the transition, the result
is $2.5 billion.
Additionally, an implementation of the hierarchical clustering algorithm along with
the proposed optimizations are presented. The hierarchical clustering algorithm is utilized
to clustering the blocks within the ultimate pit limit and it successfully reduces the
problem size of open-pit mining by 85%. The implementation with the clustering
algorithm output proves that the hierarchical clustering algorithm is capable of reducing
the open-pit problem size and improve solution time. Along with the result of the
hierarchical clustering algorithm, the proposed Transition Point Model and Transition
Period Model have generated the result of approximately $191 million of undiscounted
cashflow and $146 million of net present value, respectively.
In conclusion, two mathematical models have been developed, validated, and
implemented in case studies. Besides, two-scale reduction strategies are incorporated into
the research to manage the scale issue. It is proved that the models can solve the transition
problem by maximizing the value of the project.
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1.1 PROBLEM DESCRIPTION
Open-pit mining is the most broadly applied mining strategy as it is generally
and economically superior to underground mining methods. Open-pit mining is
preferable because of its numerous advantages such as mining recovery, production
capacity, mining capacity, dilution, safety and others. However, it leaves a large
mining footprint and leads to environmental and social unfriendliness. Additionally,
open-pit mining method is only suitable for shallow deposits due to its sensitivity
to haulage and stripping costs.
In contrast, underground mining is more favorable in the social and
environmental perspectives as it creates less disturbance to the earth topography.
However, due to its higher mining cost than open-pit mining method, it needs to be
more selective by minimizing the waste movement from underground to surface.
Furthermore, underground mining requires huge up-front investment cost for pre-
production development such as decline, ore drives and ventilation. Besides,
underground mining has more complex mine operations in terms of production,
planning, environment, and safety. Hence, underground mining is usually
applicable for deep deposits where open-pit mining cost outweighs the underground
mining cost.
There are some shallow deposits which change considerably in geometry along
the strike. Most of these deposits are often planned and mined using open-pit mining.
Afterwards, when these deposits become burdened with excessive stripping,
transiting to underground mining then becomes a viable strategy to extract the
remaining reserves. The implementation of both open-pit and underground mining
methods for ore mining purposes is known as the combination of open-pit and
underground mining strategy.
Conventionally, during the planning stage, open-pit and underground mining are
often studied individually, e.g. start with open-pit mine project and initiate the
underground mine study at a later stage. However, this approach will directly
impact the value of the project and its resource utilization due to the arbitrary
decision-making on crown pillar location and transition period. For instance, in
some cases, if transition took place in an earlier stage, better economic outcome
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could have been possible. In the past decades, very few studies have been conducted
to optimize the mine planning for the combination of open-pit and underground
mining strategy which integrates both open-pit and underground mine planning into
a single approach to maximize the resource utilization and mine project value.
The shallow deposits that extend to a considerable depth may potentially
experience a ‘Transition Problem’. The transition problem emerges when the
decision needs to be made about whether to (1) expand the pit, (2) switch to
underground mining to recover the deeper part of the deposit or (3) cease the mining
operation. Thus, the transition problem is an indication of when and where to make
the transition to capitalize on the value of the project. In this respect, the timing of
the transition is known as ‘Transition Period’ while, the location to switch to
underground mining is known as ‘Transition Point’.
With the option (1) and (2) in place, the first option will incur significant haulage
and stripping costs due to the large pit cutback and the second option may be the
optimal strategy for the remainder of the deposit at a greater depth, as its mining
cost is not as sensitive to depth as the open-pit mining method. Figure 1-1 shows
the schematic of combination of open-pit and underground mining strategy and
transition problem.
Figure 1-1: Schematic of combination of open-pit and underground mining strategy and transition
problem (Chung, Topal, and Ghosh 2016)
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The accomplishment of an optimal mine plan for the combination of open-pit
and underground mining strategy is possible only if the feasibility of the study stage
of the project establishes the optimal transition point and optimal transition period.
Ideally, in the practice of the combination of open-pit and underground mining
strategy, open-pit mine operation should cease when:
• open-pit mining cost is greater than underground mining cost;
• crown pillar location is considered and optimized;
• resource and reserve distribution are optimized.
In the case that underground mining method is neglected as the viable strategy
at the initial stage, significant issues will emerge while completing the mine study
for transition problem. The first issue is the crown pillar location. Ideally, the crown
pillar should be located at the level or location with the least revenue (i.e. low-grade
ore). However, in the conventional approach, the initial defined ultimate pit limit
(UPL) will drive the crown pillar placement. This situation forces the crown pillar
location to be arbitrary in the decision-making process. Due to the static crown
pillar location, it may lead to two consequences which are loss of reserves and loss
of project value.
Figure 1-2 shows a schematic of the resource distribution. Following the
discussions above and schematic presented in Figure 1-2, a robust mine planning
and optimization tool which can outline the resource distribution for open-pit and
underground mining is required. The tool must consider the following aspects to
ensure its practicality:
i. the integration of both open-pit and underground mining strategy and
schedule;
ii. the ability to determine the optimal mining strategy for the mine project;
iii. the location of crown pillar;
iv. the capital required for underground development;
v. smooth transition from open-pit to underground mining;
vi. the ability to schedule production delays during transition; if required.
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Figure 1-2: Schematic of resource distribution for combination of open-pit and underground
mining strategy (Chung, Topal, and Ghosh 2016)
1.2 RESEARCH OBJECTIVES AND MOTIVATION
The primary goal of this research is to construct and implement mathematical
models for the combination of open-pit and underground mining strategy which can
resolve the transition problem while satisfying open-pit and underground mining
constraints. The constraints including, but not limited to, reserve constraints, open-
pit block sequence, underground mine design restrictions, underground vertical
access limitations and crown pillar placement. Besides, the expected subsidiary
outcome of the research will be able to provide guidance on an optimal mining
strategy.
The objective of this research was reached through the following steps:
• Review the established approaches regarding the transition problem;
• Develop optimal and reliable mathematical programming models to
determine the optimal transition point and transition period;
• Incorporate production delay option throughout the transition from open-pit
to underground mining.
The utilization of a mathematical model to solve the complex transition problem
is urged due to its performance. However, generally, mathematical models are
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computationally complex due to a large number of decision variables which lead to
difficulty in solving these large-scale and NP-hard optimization problems. In order
to handle the scale issue, the secondary objective of this research is to introduce
data clustering approach that will reduce the number of decision variables in the
mathematical model for the transition problem.
The motivation of this research originates from the often overlooked
simultaneous mine planning and optimization process which combines open-pit and
underground mining strategies in the past decades. In cases where a combination of
open-pit and underground mining strategy can be practiced, a conventional
approach (i.e. study open-pit and underground mining individually by initiating
open-pit mine study first) is often preferred or chosen. The conventional approach
tends to ignore the ‘best’ resource distribution for the deposit which leads to sub-
optimal project value and reserve utilization.
1.3 ORIGINAL CONTRIBUTIONS OF THIS RESEARCH
The scope of this research project is limited to optimizing the transition problem
for the combination of open-pit and underground mining strategy that maximizes
the net present value (NPV) and generates an optimal mining layout for a mining
operation. It aims to define the optimal transition point, subsequently, providing a
transition schedule for the combination of open-pit and underground mining
strategy. Additionally, to solve this NP-hard transition problem, development and
implementation of a brand-new hierarchical clustering algorithm is formed as part
of the scope in order to handle the large-scale problem. Commonly, input values to
the models are subjected to uncertainty. Hence, those inputs can influence the
reliability of the result that lies outside the scope of the study.
1.4 SIGNIFICANCE AND RELEVANCE
In the last decades, as many open-pit mines are reaching their critical stage, the
transition problem becomes one of the most significant engineering issues for
mining engineers. In addition, due to the increased demand for raw materials, the
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transition problem has been prioritized to ensure the continuity of the mining
activities. There are a few examples of mines that have made the transition from
surface to underground mines such as Chuquicamata mine in Chile (Flores and
Catalan 2019), Grasberg mine in Indonesia (Sulistyo, Soedjarno, and Simatupang
2015) and Sunrise Dam in Western Australia (Opoku and Musingwini 2013). Hence,
this research project offers a new approach towards the planning and optimization
of the transition problem which benefits the mining industry in several aspects such
as:
• maximize resource utilization;
• maximize project value;
• improve life-of-mine (LoM);
• smooth transition from open-pit to underground;
• schedule production delay or interruption during transition within LoM plan,
if required.
1.5 THESIS OVERVIEW
The remainder of this thesis is divided into six chapters which are:
Chapter 2 studies the relevant literature in open-pit mining, underground mining
and combination of open-pit and underground mining strategy. The chapter also
discusses the challenges of the proposed model and tactics to handle the issues
along with its relevant literature.
Chapter 3 presents the mathematical formulations for the transition point and
transition period, which focus on the determination of the transition point and
transition period. A validation process of the model is also included in this chapter.
Chapter 4 explores the implementation of the mathematical model using exact
methods presented in Chapter 3 and establishes the computational complexity in
realistic data sets.
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2.1 MINING PROCESS
A typical mining process starts from exploration, followed by orebody
modelling. During the orebody modelling stage, a geological block model is
generated. Then, the geological block model is transformed into an economic block
model with consideration of economic and technical factors such as commodity
price, recovery rate, mining cost and others.
The economic block model is used to complete the mine planning and
optimization process. During the earliest stage of mine planning and optimization,
it is often questioned about the most appropriate mining method (Topal 2008).
Generally, the preferred mining method is pre-selected based on the knowledge of
the engineer or characteristics of the orebody. Then, taking account of the selected
parameters and capacities such as mining capacity and processing capacity, a
mining layout and plan of extraction are produced. The mine planning and
optimization process are critical as they provide guidance on how to extract the
valuable material and attempt to optimize the project value over the LoM (Dagdelen
and Johnson 1986; Caccetta 2007). The last step of the mining process is the
execution of the plan.
2.2 OPEN-PIT AND UNDERGROUND MINE PLANNING AND
SCHEDULING
Mine planning and optimization play a critical role in the mining process. This
process directly, and indirectly, impacts the economic prospect of the project.
Nowadays, numerous mine planning and optimization methodologies, techniques
and approaches are available for open-pit and underground mining. The available
techniques and approaches for each mining method will be discussed in the
following sections.
2.2.1 Open-pit mining
In open-pit mining, UPL optimization is aimed at defining the size of extraction
and volume of extracted material that maximizes the undiscounted value of a project
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subjected to pit slope ore precedence requirements. The general idea is to make sure
that a given block is only extracted if the precedence blocks have been extracted.
In the past decades, the three most notable methods to define the UPL are the
floating cone (FC) method (Carlson et al. 1966), Lerchs and Grossmann (LG)
method (Lerchs and Grossman 1964; Whittle 1990) and Pseudoflow method
(Hochbaum and Chen 2000; Hochbaum 2001).
The FC is a heuristic approach which involves an iterative process. This method
searches through the block model by assessing the value of the cone. The FC
method is rarely used by the mining industry these days due to the lack of flexibility
of the algorithm. It is unable to detect the mutual support among the different parts
of the orebody, and it only considers those blocks within the cone. The LG
algorithm (Whittle 1990) is the most notable algorithm which provides a
computational and tractable method for open-pit mining layout optimization. The
LG algorithm is based on graph theory. It aims to define the maximum closure of a
weighted directed graph by using a maximum-weight closure algorithm to
maximize profit. Hence, the vertices, weights and arcs in the algorithm represent
the mining blocks, net profit, and slope constraints respectively. Likewise, the
Pseudoflow method (Hochbaum and Chen 2000; Hochbaum 2001) is the most
recent developed algorithm and it is widely utilized by many mine optimization
software. The Pseudoflow algorithm inherited the LG algorithm normalized trees
and further developed it to a general network flow model. It solves the maximum
flow model on general graphs, hence, it is generally more computationally efficient
compared to the LG algorithm.
Open-pit scheduling is the next process after the generation of UPL. This
scheduling process defines the sequence of production that maximizes the
discounted value of the operation while satisfying precedence and operational
capacity constraints. Some formulations also include grade control and stockpile
constraints. Most of the current available literature, can be divided into two main
groups namely heuristic algorithms or exact mathematical models (Askari-Nasab,
Awuah-Offei, and Eivazy 2010).
Various intelligence-based algorithms have been presented in the past. Some of
the notable works in this area are proposed by Tolwinski and Underwood (1992),
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Denby and Schofield (1994), Askari-Nasab (2006) and Askari-Nasab and Awuah-
Offei (2009). Tolwinski and Underwood (1992) suggested an approach which
integrated dynamic programming, stochastic optimization and machine learning
which was successfully implemented by Elevli (1995). Meanwhile, Denby and
Schofield (1994) developed a genetic algorithm for the UPL and production
scheduling problem. The recommended algorithm starts by populating random pits
and then, assesses the function of the fitness of the populated pits. The algorithm is
an iterative process as it stops when re-occurrence of a state happened, and no
further improvement is generated. The major drawback of the heuristic-based
algorithms is that the optimally of the solution is unable to be measured. In addition,
most of the results are also unable to be reproduced since they are probability-based.
Furthermore, many operations research (OR) based methodologies such as linear
programming (LP) and mixed-integer linear programming (MILP) are presented to
solve the open-pit scheduling problem. There are several reasons as to why MILP
and Integer Programming (IP) are attractive and there are:
• Cut-off grade can be optimized as it allows the model to determine if the
material is mined and the mineable material is treated as ore or waste.
• They can integrate the optimization of a user-defined weighted function of
the life-of-mine and NPV.
• They are flexible to cater for complex mine operations such as multiple
products, destinations, and sites.
• They have the sensitivity analysis capability.
Johnson (1968) developed the first LP model for open-pit scheduling problem,
which inspired Gershon (1987) to create a MILP model on the open-pit scheduling
problem. Other than that, there are some noteworthy models that include, but are
not limited to, Caccetta and Hill (1999), Dagdelen and Kawahata (2007), Askari-
Nasab, Awuah-Offei, and Eivazy (2010), Eivazy and Askari-Nasab (2012) and
others. However, due to the scale of the open-pit problem, the problem becomes
computationally intractable. Hence, a variety of methods have been proposed to
handle the large-scale problem such as the reduction of the number of binary
integers as suggested by Ramazan and Dimitrakopoulos (2004) and the Lagrangian
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relaxation method proposed by Dagdelen and Johnson (1986). Ramazan and
Dimitrakopoulos (2004) introduced a new MILP method that intended to reduce the
number of binary variables by considering two aspects: (1) only positive value
blocks defined as binary and (2) remaining variables are defined as linear.
Additionally, Dagdelen and Johnson (1986) presented a Lagrangian relaxation
method which uses the Lagrangian multipliers to decompose the complex problem
into smaller problems, for instance, by solving the long-term open-pit optimization
problem by decomposing the multi-period problem into multiple single-period
problems.
2.2.2 Underground mining
In underground mine planning and optimization, the main components that are
responsive to the optimization process are stope boundary optimization,
development placement and production scheduling (Little 2012). This research
project will focus on two components which are stope boundary and production
scheduling. Defining an optimal stope layout is one of the important tasks in
underground mine planning. Stope layout is known as a group of blocks that lies
within an envelope and they are economical to be extracted as a whole. Meanwhile,
stope layout optimization is a process to obtain the best combination of blocks to
form stopes within the block model which generates the best project values and
reserve utilization. As a result, the set of profitable stopes which has the highest
return will form an underground mining layout. Numerous approaches have been
presented to optimize the stope layout. Some of the noteworthy algorithms were
developed by Alford (1995), Ataee-Pour (2004), and Grieco and Dimitrakopoulos
(2007).
The FS algorithm is the most well-known stope layout algorithm presented by
Alford (1995). The FS algorithm used a sophisticated, rectangular block as the
minimum stope size that is floated through the block model. This algorithm has
been improved and developed as the Vulcan Stope Optimizer (Maptek 2011). The
Maximum Value Neighborhood (MVN) algorithm is another stope layout
optimization method which was introduced by Ataee-Pour (2004). This algorithm
is a heuristic-based approach which defines stope boundary by assessing the best
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neighbourhood for each block. With the possible combination of neighbourhood,
the one with the maximum value is chosen. Grieco and Dimitrakopoulos (2007)
presented a probabilistic mathematical programming model to solve the stope
layout optimization. MILP model is developed to determine a stope size based on
the number of blast rings being included in a stope. Additionally, there are other
studies for underground stope layout design problem included, but are not limited
to, the octree division algorithm (Cheimanoff, Deliac, and Mallet 1989), Stopesizor
algorithm (Alford, Brazil, and Lee 2007), and the transformed stope boundary
optimization (Topal and Sens 2010).
Apart from stope layout design, long-term underground mine production
scheduling is important. Numerous approaches and algorithms are available in this
respect. MILP and IP play a significant role in long-term underground production
scheduling optimization. Over the years, many mathematical models have been
developed to the optimize underground production scheduling problem. Those
notable works include, but are not limited to Trout (1995), Topal (2008), Nehring
et al. (2010), and Little and Topal (2011).
Trout (1995) developed a MILP model to obtain the optimal production
sequence for a sublevel stoping method. The aim of the model is to maximize the
NPV of the mining operation. This model was implemented on a copper operation
and its efficiency proved. Nehring and Topal (2007) enhanced the MILP model by
introducing a new formulation for limiting multiple exposure of fill masses.
Following that, Topal (2008) introduced variable reduction strategies associated
with MILP model which has increased the efficiency of the mathematical model.
Two strategies have been introduced: which are defining (1) machine limitations
and (2) introducing early and late start algorithm to narrow the observation period
for the machine placement. Implementation has been demonstrated by using the
Kiruna Mine dataset where significant reduction of variables resulted in increased
computational efficiency. Besides, Nehring et al. (2010) presented a MILP model
which integrates short-term and long-term production scheduling concurrently. The
objective function consists of minimizing the deviation of mill feed grade in a short-
term schedule, while maximising NPV in the long-term schedule and cash penalties
for feed grade to ensure operational and recovery efficiency. Moreover, Little and
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Topal (2011) proposed an IP model for stope layout and production scheduling
optimization concurrently with the objective to maximize the NPV of the operation.
The authors proposed two concepts to minimise the number of integer variables,
such as combining blocks into a potential stope and removing negative value stopes.
Many approaches for both layout and production schedule optimization have
been present for open-pit and underground mining method in the last decades.
However, the optimal solution for realistic open-pit production scheduling
optimization remains impossible. Hence, continuous efforts are required to improve
the optimization process and to obtain the optimal schedule for open-pit within
reasonable timeframes.
On the other hand, a mathematical model is advantageous for both underground
mining layout optimization and production scheduling optimization. It guarantees
the optimal solution and helps to ensure efficiency of the mine operations. However,
the number of variables involved in a mathematical model are critical and it should
be kept at the minimal level at all the time.
2.3 TRANSITION FROM OPEN-PIT TO UNDERGROUND -
COMBINATION OF OPEN-PIT AND UNDERGROUND MINING
STRATEGY
Apart from the conventional approach (Section 2-1), a few studies (Nilsson 1992;
Camus 1992; Arnold 1996; Tulp 1998; Fuentes 2004; Brannon, Casten, and
Johnson 2004; Fiscor 2010) share approaches and algorithms to solve the transition
from open-pit to underground mining.
Soderberg and Rausch (1968) introduced a surface-to-underground stripping
ratio approach that delineates mining cost, ore recovery and dilution which suggests
that these are the controlling factors for the transition problem. It proposed a
breakeven cost differential relationship in Equation (2-1) that accounts for open-pit
mining cost per tonne of ore (𝑚 ), underground mining cost per tonne of ore
𝑂𝑃
(𝑚 ), and the open-pit waste stripping cost per tonne of waste(𝑤 ) and
𝑈𝐺 𝑂𝑃
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calculates the indicated stripping ratio (𝐼𝑆𝑅). Accordingly, if the stripping ratio
corresponding to a mining block is less than 𝐼𝑆𝑅 in Equation (2-1), then open-pit
mining would be economical, otherwise underground mining becomes economical.
𝐼𝑆𝑅 =
𝑚𝑈𝐺−𝑚𝑂𝑃
(2-1)
𝑤𝑂𝑃
Nilsson (1982, 1992) proposed a cash flow analysis-based trial and error method
that relies on the experience of a mine planning specialist. The author suggested the
aspects which need to take into consideration and may influence the transition
problem such as stripping ratio, interest rates and production costs. However, this
approach is purely based on the knowledge of the mine planner. Hence, it does not
describe by any optimization tactic. Abdollahisharif et al. (2008) modified the
Nilsson (1982, 1992) method and applied an iterative approach that accounts for
alternative crown pillar locations and selects the best among these feasible
alternatives as the transition point.
Camus (1992) applied the Lerchs and Grossmann (1965) algorithm implemented
on a modified economic block model. The block value is calculated by a modified
economic block value (𝐸𝑉 ) accounting equation. The modified accounting
𝑚
equation integrates profit, open-pit cost and underground mining cost, as present in
Equation (2-2). Hence, each block has to be able to pay both open-pit stripping cost
and potential underground benefit if it needs to be mined through open-pit mining
or, vice versa. For instance, if the profit and stripping cost for open-pit is $50 and
$20 respectively, the block value for open-pit mining is $30 (𝐵𝑙𝑜𝑐𝑘 𝑉𝑎𝑙𝑢𝑒 ).
𝑜𝑝𝑒𝑛 𝑝𝑖𝑡
For the same block, if the underground block value is $20
(𝐵𝑙𝑜𝑐𝑘 𝑉𝑎𝑙𝑢𝑒 ), the modified block value is $10 (𝐸𝑉 ). In this case,
𝑢𝑛𝑑𝑒𝑟𝑔𝑟𝑜𝑢𝑛𝑑 𝑚
open-pit is the optimal mining method for the block. On the flip side, if 𝐸𝑉 is less
𝑚
than zero, underground mining method is the optimal mining method for the block.
Camus (1992) claimed that the UPL generated using this modified economic block
model provides the location (transition point) to switch from open-pit to
underground operation.
𝐸𝑉 = 𝐵𝑙𝑜𝑐𝑘 𝑉𝑎𝑙𝑢𝑒 −𝐵𝑙𝑜𝑐𝑘 𝑉𝑎𝑙𝑢𝑒 (2-2)
𝑚 𝑜𝑝𝑒𝑛 𝑝𝑖𝑡 𝑢𝑛𝑑𝑒𝑟𝑔𝑟𝑜𝑢𝑛𝑑
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Bakhtavar, Shahriar, and Oraee (2008) proposed a heuristic algorithm that
maximizes the undiscounted value from both open-pit and underground mining.
The approach keeps the first three levels in an open-pit operation and compares the
value of the remaining levels for both open-pit and underground options. When the
underground mining value is higher than open-pit mining, the last level of the pit is
divided into sublevels and then the comparison is re-run. Transition from open-pit
to underground happens when underground mining generates a higher value on the
level than open-pit mining. The method can determine the open-pit layout,
transition point, location of the crown pillar and a profile of underground levels.
Bakhtavar, Shahriar, and Mirhassani (2012) presented a two-dimensional IP
based mathematical model to resolve the transition problem. This model aims to
maximize the undiscounted value of the transition from open-pit to underground
mining by catering for an objective function that includes both open-pit (𝑜𝑝𝑏𝑣 )
𝑎
and underground value (𝑢𝑔𝑏𝑣 ) of a block as shown in Equation (2-3). The
𝑎
constraints taken into consideration in the model include reserve restriction
constraints, slope constraints, minimum stope width and height constraints,
maximum stope width and height constraints, crown pillar constraints and level-
based reserve restriction (‘at most one method for each row’) constraints. The
proposed model has successfully demonstrated the complexities of the transition
problem and guaranteed optimality. However, it is unable to be implemented in real
applications due to the computational cost.
𝑂𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛: 𝑍 = max∑𝑜𝑝𝑏𝑣 +𝑢𝑔𝑏𝑣 (2-3)
𝑎 𝑎
Roberts et al. (2013) proposed an iterative process that applies the incremental
value concept that ranks mining blocks to establish their potential for open-pit or
underground mining. In this respect, the incremental value of a block (𝐼𝑉 ) is the
𝑎
difference between the discounted value per tonne of a block if mined by
underground (𝑈𝐺𝐷𝑉 ) and the discounted value per tonne of block if mined by
𝑎
open-pit mining (𝑂𝑃𝐷𝑉 ), as presented in Equation (2-4). The underground
𝑎
discounted value per tonne of a block (𝑈𝐺𝐷𝑉 ) is calculated based on an equation
𝑎
by taking into account various important parameters such as net revenue of a block
(𝑟 ), processing cost for underground operation (𝑝 ), mining cost (𝑚 ) and cost
𝑎 𝑢𝑔 𝑢𝑔
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associated with avoiding underground mining (𝑣). On the other hand, the open-pit
discounted value per tonne of a block (𝑂𝑃𝐷𝑉 ) is the maximum function of the
𝑎
discounted profit of open-pit mining which only includes net revenue of a block (𝑟 )
𝑎
and processing cost for open-pit operation (𝑝 ). The equations for discounted value
𝑜𝑝
accounting for underground and open-pit mining are presented in Equation (2-5)
and (2-6), respectively. Therefore, the positive and higher incremental value
indicates the suitability of a block for underground mining and a negative
incremental value which indicates the suitability of block for open-pit mining.
𝐼𝑉 = 𝑈𝐺𝐷𝑉 −𝑂𝑃𝐷𝑉 (2-4)
𝑎 𝑎 𝑎
𝑈𝐺𝐷𝑉 =
𝑟𝑎−𝑝𝑢𝑔−𝑚𝑢𝑔− 𝑣
(2-5)
𝑎 (1+𝑑)𝑢𝑦 (1+𝑑)𝑜𝑦
𝑂𝑃𝐷𝑉 = max
(𝑟𝑎−𝑝𝑜𝑝
,0) (2-6)
𝑎 (1+𝑑)𝑜𝑦
where
𝑑 discount rate
𝑜𝑦 year in which block is mined through open-pit
𝑢𝑦 year in which block is mined through underground
Opoku and Musingwini (2013) introduced a structured methodology towards
solving the transition problem. Initially, the procedure applies open-pit mining for
the entire mineral resource, then it applies the option to switch from open-pit to
underground mining and finally applies the option for underground mining for the
entire mineral resource. Finally, it applies NPV, stripping ratio, average grade,
refined metal as indicators to rank the three options and selects the option with
highest rank.
Dagdelen and Traore (2014) applied a sequential procedure for the transition
problem. The procedure creates a UPL through the Whittle commercial mine
planning software, defines the underground stope layout using Studio 5 and EPS
software and then finally applies OptiMine scheduler to define the production
schedule over life of operation. However, this sequential procedure is prone to sub-
optimality with issues around the location of a crown pillar.
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Whittle et al. (2018) developed a UPL optimization algorithm while solving the
transition problem at the same time. The authors framed a maximum graph closure
problem which can define the optimal mine outline for the combination of open-pit
and underground mining strategy. Digraph is used to tackle the problem which is
similar to Whittle (1990). However, Whittle et al. (2018) included two more types
of arcs to cover the underground mining option. The first type of arc is to bring
underground opportunity cost into the optimization problem. Hence, the tail of the
arc is in the open-pit vertices and the head is in the offset underground vertices (Z-
elevation). The elevation offset is to accommodate the crown pillar requirement.
Furthermore, the second type of arc is to satisfy the overall underground crown
design requirement. A non-trivial strongly connected subgraph is introduced to
achieve a prescribed shape.
In the past, very limited studies have been conducted to obtain the optimal
transition period or the optimal production schedule for combination of open-pit
and underground mining strategy due to the issues of complexity and scale of the
problem. Newman, Yano, and Rubio (2013) successfully demonstrated how to
solve the large longest-path problem by a series of small longest-path problems.
The aim of the study is to maximize the NPV which takes the discounted profit
from the mined strata (level) less the discounted underground infrastructure cost if
strata is extracted through underground mining. From the study conducted by
Newman, Yano, and Rubio (2013), a large network formulation that represents the
transition problem has been presented in the first place. Due to the complexity of
the problem, the authors suggested to decompose the large longest-path problem
into a series of smaller networks which take advantages of the underlying
composition of the problem. Besides, the authors also placed some rules during the
construction of the simpler network to ensure that the series of networks are
collective and compressed as much as possible. This approach is flexible as the user
can choose to remove any impractical nodes or arcs which reduces the size of the
problem. However, the drawback of this approach is the lack of practicality due to
the utilization of a level-based concept.
Khaboushan, Osanloo, and Esfahanipour (2020) presented a heuristic-based
process that optimizes the NPV of a mining project. The proposed process starts
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from UPL generation and then, generates a series of transition scenarios within the
generated UPL. Underground mining method is assigned for the resource that lies
below the UPL. Then, the authors generated a production schedule and maximized
NPV for each of the transition scenarios. Finally, the authors compared the results
and selected the best scenario which is the scenario which returns the highest NPV.
With the needs of solving the transition problem optimally, this research is
committed to construct a robust model to solve the transition problem. The primary
objective of this research project is to build an optimization tool that can solve the
transition problem by satisfying both open-pit and underground mining constraints.
These constraints include, but are not limited to reserve constraints and mining
sequence constraints for open-pit mining, mine design restrictions and vertical
access limitations for underground mining and crown pillar positioning. Also, the
subsidiary outcome of this research is the ability to provide mine planning and
optimization guidance for the combination of open-pit and underground mining
strategy.
2.4 CLUSTERING TECHNIQUES
In the past, numerous algorithms have been introduced for block aggregation
purposes in the mining industry. The clustering technique is an effective way to
handle large-scale optimization problems. Clustering is a process in which a
partition or aggregation of a set of entities is made into similar groups based on
calculated or defined similarity index between each pair of data. The main idea of
clustering is to decrease the size of the data which translates to reduction in size of
the problem. Although the clustering algorithm generates sub-optimal result for the
mine optimization problem, the drastic improvement on computational time for the
mathematical model has been proved (Ren and Topal 2014).
The similarity index plays a significant part in the clustering process. It can be
used on various properties. Besides, it offers flexibility which is able to be
customized as requirements. However, the number of properties involved in the
similarity index calculation may exponentially increase the difficulty and
complexity of the index. In the mining industry, the most common settings of
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similarity index are block location, grade, rock type and inter-relationship between
clusters (Askari-Nasab et al. 2010).
Hierarchical clustering is one of the most widely used clustering techniques.
There are two methods to form cluster trees in a hierarchical clustering algorithm
which are agglomerative and divisive (Askari-Nasab et al. 2010). The hierarchical
agglomerative clustering algorithm considers each object as a cluster and it starts to
aggregate them into a new group. The brief overview of agglomerative clustering
algorithm is as below (Jain, Murty, and Flynn 1999; Johnson 1967):
• Step 1: Compute the proximity matrix and treat each entity as a class;
• Step 2: Seek for the most similar pair of the entities and group them into the
same group and form the new cluster. Update the proximity matrix;
• Step 3: Stop, if only one cluster left. Otherwise, go to Step 2.
The divisive hierarchical clustering algorithm performs in a top-down fashion
which considers the whole set of entities as a single cluster and splits the cluster to
form a new group interactively. It stops when the desired number of clusters are
reached (Jain, Murty, and Flynn 1999).
Askari-Nasab et al. (2010) presented a hierarchical clustering algorithm for
open-pit mines with the aim of diminishing the number of variables of the MILP
model. The MILP formulation utilized for production scheduling purposes consists
of lower and upper bounds for the grade blending, mining and processing capacity,
reserve constraints and precedence relationship rules. The objective function of the
MILP model maximized the discounted value (Askari-Nasab et al. 2010; Askari-
Nasab, Awuah-Offei, and Eivazy 2010). For the clustering algorithm, four
attributes are proposed to be incorporated in the similarity index. The attributes are
location, grade, rock type and beneath cluster as described below:
• Location: To avoid impractical block aggregation as opposed to location
such as aggregation of blocks which are far apart;
• Grade: To prevent significant grade deviation among blocks within a cluster
as uniform grade is considered in the production scheduling optimization;
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• Rock type: To differentiate the ultimate destination of the materials; waste
rock will be directed to the waste dump and ore will be directed to the
processing plant or stockpile;
• Beneath cluster: To form clusters on top of each other which can avoid
mining too much low-grade ore or waste material at any time in order to
reach high-value clusters.
The proposed calculation of the similarity index for two blocks (block i and j) is
as shown in Equation (2-7).
S =
Rij×Cij
(2-7)
ij D̃ iW jD ×G̃ iW jG
where,
S Similarity index for blocks
ij
R Rock type similarity factor
ij
C Penalty factor for blocks which are below different clusters
ij
D̃WD Normalised distance factor
ij
G̃WG Normalised grade difference factor
ij
WD Weight of distance factor
WG Weight of grade factor
The proposed algorithm assumed that each individual block within the pit as is
treated as part of a cluster. The most similar and adjacent blocks merge together
and form a cluster with a new calculated similarity index. Then, run the algorithm
again by selecting the next ‘perfect match’ blocks. This process repeats until the
defined number of clusters is attained. The authors used an adjacency matrix and
updated the matrix to accelerate the running time of the algorithm. A case study
was also presented by Askari-Nasab et al. (2010) to demonstate use of the algorithm.
Although this method has successfully reduced the problem size, intensive
processing time is required as it has to run the algorithm at every level in the pit.
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Tabesh and Askari-Nasab (2011) introduced a two-stage clustering algorithm to
address the optimization of open-pit production scheduling scale issue. The first
stage is to adopt the hierarchical algorithm which was proposed by Askari-Nasab
et al. (2010). The second stage is to utilize the Tabu Search method to re-evaluate
the clusters formed by the first stage. The aim of the second stage is to reduce the
binary constraints.
The concept of the second stage is to visit the clusters formed from the first stage
and seek for opportunity to detach any of the clusters and attach to the neighbouring
cluster. When exploring for opportunity, the main rule is not to break the bond of
the current clusters if detachment is exercised. This second stage is advantageous,
particularly for those blocks located at the border of the clusters.
Moreover, a ‘state measure’ is introduced which helps to achieve good and
healthy relationship between similarity and arcs of clusters. The state measure is
based on average intra-cluster similarity and number of arcs as it is presented in
Equation (2-8) as follows:
Normalised average of all intracluster similarities
State measure = (2-8)
Normalised number of arcs
The tabu search based clustering scheme is firstly to evaluate the result generated
by the hierarchical clustering algorithm and the number of arcs for each entity. Then,
it evaluates the relationship between clusters and the immediate clusters beneath it.
The process runs iteratively to assess the most dependent block and seek for
opportunity to attach to the neighbouring clusters. The case study presented by
Askari-Nasab et al. (2010) was used to compare the MILP result. The proposed
two-stage clustering method successfully improved the number of coefficient
matrix size by 1% and non-zero elements number by 2%. However, it also degraded
the MILP result.
Ramazan (2001), Ramazan, Dagdelen, and Johnson (2005) and Ramazan (2007)
introduced the fundamental tree algorithm (FTA) to reduce the number of binary
integers and constraints within the linear programming model. FTA is a linear
programming-based model that aims to aggregate blocks. The conditional
properties of FTA are:
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• Positive economic value post-cluster;
• Ability to mine the post-cluster without violating slope requirements;
• Cluster cannot be detached after aggregation without compromising the
above conditions.
The aggregated blocks are known as a ‘fundamental tree’. Prior to FTA, a cone
template which represents the wall slope angle requirement is needed in order to
evaluate the deposit. The fundamental trees are formed within a pushback. Those
trees with a negative value are treated as waste clusters. Besides, the precedence
relationships among clusters are determined.
In the FTA, there are five steps to execute which are:
• First step: Seek for a cone value for each pushback or ultimate pit. The
economic value of each block is known as a ‘cone value’ (CV) and is given
by Equation (2-9).
Net revenue of i - Mining cost of i - Processing cost of block i; if ore
CV={ (2-9)
i - Mining cost of i; if waste
• Second step: Assign a coefficient to each ore block to represent its ranking
by bench. A ranking system is utilized to perform on-bench based ranking.
If two cones with the same cone value exist, a random coefficient will be
assigned; hence, no repeated coefficient will be assigned.
• Step three: Setting the mathematical formulation for the FTA and solve
mathematical model to generate fundamental trees.
• Step four: If the number of trees generated is greater than the preceding
solution, then run the process again. This process will be running iteratively
until the number of trees generated is equal to the former result which will
then be considered as optimal. The two-dimensional illustration for FTA is
presented by Ramazan (2007) and Ramazan, Dagdelen, and Johnson (2005).
• Step five: Develop and solve the MILP prototype for open-pit production
scheduling optimization.
Ramazan, Dagdelen, and Johnson (2005) presented a case study on a multi-
element copper deposit. In the case study, the authors successfully decreased the
number of binary variables by 85%. The result generated was compared to three
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traditional mine scheduling software. The undiscounted cashflows generated by
two of the scheduling tools are higher than the proposed algorithm. However, the
total NPV for the proposed algorithm returns the highest.
Mai (2017) and Mai, Topal, and Erten (2018) further developed the FTA into
the TopCone Algorithm (TCA) which aggregates blocks into TopCones (TCs). The
authors adopted the framework presented by Ramazan (2007) and advanced the
algorithm by including the ability to maintain slope shape and able to control the
number of TCs. In order to achieve those enhancements, the authors introduced four
qualifications that TCs need to satisfy which are: (1) can be unearthed by not
violating the slope restrictions, (2) return positive value of TC, (3) satisfy certain
constraints such as minimum cone size and (4) TC cannot be fragmented into a
smaller size without violating the forementioned qualifications (1-3). As the TCA
is able to obey the minimum number of blocks per TC, the framework can be
implemented to any real and large-scale problem. The authors implemented the
TCA in a block model that contains 1.5 million blocks and compared the result with
the Whittle Milawa NPV algorithm. The TCA returned a higher NPV by
approximately 7%.
2.5 RESEARCH METHODOLOGY
Throughout the literature review, there is no evident track that any of the
available presented methods can solve the transition problem optimally. The main
reasons can be traced from the complexity of the transition problem, computational
cost and scale of problem. Ultimately, a tool that can deal with both open-pit and
underground mine planning and optimization concurrently is required to solve the
transition problem.
The proposed research methodology to develop a solution to the problem is as
follows:
1. Mathematical modelling method is proposed to solve the transition
problem.
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• Develop mathematical model to solve transition point and generate
undiscounted project value for the mine operation – transition model.
• Enhance transition model to determine both optimal transition point
and optimal transition period. The objective is to maximize the NPV
of the project and minimize the capital investment cost for the
transition – transition period model.
2. Structured approach is employed to handle the problem scale concern for
underground mining.
• Implement stope-based methodology introduced by Little and Topal
(2011) to reduce the problem size.
3. Hierarchical clustering algorithm is selected for open-pit scale reduction
purposes.
• Aggregate open-pit blocks by evaluating the similarity of a group of
blocks to reduce the open-pit decision variables.
2.6 SUMMARY
Literature has demonstrated the significance of solving the transition problem
and many tactics have been presented to solve the transition problem. However,
none of them can generate the optimal solution that fulfills the physical mining
constraints in three-dimensional space. Hence, a robust tool that considers both
open-pit and underground mining simultaneously is required to solve the transition
problem. The tool should aim to define the optimal transition point and/or transition
period as required.
According to the concept of optimization for combination of open-pit and
underground mining strategy, the problem can be defined as a NP-hard problem
due to the complication of the problem nature and the scale of the problem.
Therefore, a research methodology is proposed to address the problem which aims
to generate the optimal solution.
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3.1 ASSUMPTIONS
1. All mining blocks in the three-dimensional block model are regular, i.e.,
same size in x, y and z directions.
2. The economic block value of each mining block in the block model is known
and constant.
3. The pit-wall slope requirement is to avoid the geotechnical risks such as pit-
wall failure. A conventional 45 degree pit slope is considered in this research.
Hence, to satisfy the wall slope requirement, five blocks are needed to be
extracted in order to gain access of the underlying target block.
4. For the underground mining method, this research considers sublevel
stoping method. The underground sublevel stoping mining method has been
employed by many operations in Australia for its numerous advantages. The
advantages of sublevel stoping method includes the high ore recovery rate,
lower cost in a large-scale production, and high productivity.
5. The models allow for non-simultaneous open-pit and underground mining
operations.
6. The NPV is calculated based on pre-tax and depreciation assumptions.
7. All values are in $AUD currency.
8. No ore stockpiling is included in the models.
3.2 DATA PREPARATION
3.2.1 Block model
The orebody block model is the basic geological input to the transition problem.
A three-dimensional block model contains thousands of mining blocks. Each of the
mining block consists of numerous attributes such as location, quality (grade) and
quantity (tonnage). Density is another mining block attribute. This attribute is often
used to differentiate the type of the rock and its grade. With the attributes in each
block, the dimension of each block, tonnage value and metal grade of each block
are distinct (Grobler 2015).
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Furthermore, the geological block model is transformed into an economic block
model by including economic parameters and operation-related parameters. The
simplified formula used to determine the block value for each block in the economic
block model is shown in Equation (3-1).
𝑣 = (𝑝−𝑟)𝑔𝑦−𝑐−𝑚 (3-1)
where
𝑝 = commodity price ($/unit of ore)
𝑟 = refining cost ($/unit of ore)
𝑔 = grade
𝑦 = recovery rate
𝑐 = processing cost ($/tonne of ore)
𝑚 = mining cost ($/tonne of ore)
3.2.2 Stope-based methodology for underground mining
Stope-based modelling for underground mining was introduced by Little and
Topal (2011). It is an inventive way to reduce the number of binary variables in the
mathematical model. Due to the number of binary variables (from both open-pit
and underground) involved in the MILP model for the transition problem, stope-
based modelling is adopted to decrease the number of binary variables for
underground mining. The concept of the approach is to use 2x2x2 stope design, to
combine eight blocks into one stope. Thus, only one binary variable is assigned for
each stope instead of eight binary variables for each block. The naming convention
for the stope is represented as X (the coordinate of the first and last block). By using
the example in the Figure 3-1, the stope is referred to as X (1,1,1)/ (2,2,2).
Figure 3-1: Stope based methodology naming convention (Little and Topal 2011)
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Moreover, to further reduce the binary variables for underground mining, a pre-
processing step is taken. The aim of this process is to predetermine the profitable
stopes. First and foremost, an envelope of a stope such as 2x2x2 stope envelope, is
used to go across the underground block model. This step is implemented to find
all the potential stopes within the underground block model and determine its
associated economic value. Then, only stopes with positive values are retained
while those with negative values are removed. As a result, a list of profitable stopes
is generated after the process completed. This approach aligns with the precedence
concept presented by Ramazan and Dimitrakopoulos (2004), which considers the
waste blocks as air blocks to obtain fewer binary variables. By employing this
approach, Little, Knights, and Topal (2013) successfully improved the solution time
of the problem.
3.3 TRANSITION POINT MODEL – OPTIMIZATION MODEL 1
Transition point model is developed to solve the transition problem by providing
the optimal transition point by maximizing the undiscounted profit of the mine.
3.3.1 Notations and Variables
Indices
𝑖,𝑖́ = index for blocks in open-pit mining
𝑗,𝑗́ = index for stopes in underground mining
𝑘,𝑘́ = index for mining level
𝑚 = index for mining method; =1 for open-pit mining and 2 for underground
mining
𝑜𝑝 = open-pit
𝑢𝑔 = underground
Sets
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𝐾 = set of levels in the orebody model
𝜇 = set of overlying or precedence blocks for block 𝑖
𝑖
𝐵 = set of all the stopes that share mutual blocks with stope 𝑗
𝑗
𝐿 = set of all open-pit blocks on level k
𝑜𝑝,𝑘
𝐿 = set of all underground stopes on level k
𝑢𝑔,𝑘
Parameters
𝐶 = the discounted profit to be generated by mining block 𝑖
𝑖
𝑆 = the discounted profit to be generated by mining stope 𝑗
𝑗
ℓ = number of rows that should remain as a crown pillar
𝐴 = total number of overlying blocks that need to be mined in order to extract ore
block 𝑖
Decision variables
1,if block i is mined by open−pit mining
𝑥 = {
𝑖 0,otherwise
1,if stope j is mined by underground mining
𝑦 = {
𝑗 0,otherwise
1,if level k is mined by mining method m
𝑇 = {
𝑘,𝑚 0,otherwise
1,if level k is left as a crown pillar
𝐻 = {
𝑘 0,otherwise
3.3.2 Transition Point Model Formulation
The mathematical formulation is as follows:
𝑀𝑎𝑥 𝑍 = ∑ 𝐶 𝑥 +∑ 𝑆 𝑦 (3-2)
𝑖∈𝑀 𝑖 𝑖 𝑗∈𝑁 𝑗 𝑗
𝑖 𝑗
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Subject to
𝐴∙𝑥 −∑ 𝑥 ≤ 0 ∀ 𝑖,𝑖́ ∈ 𝜇 (3-3)
𝑖 𝑖́ 𝑖́ 𝑖
𝑦 +𝑦 ≤ 1 ∀ 𝑗,𝑗́ ∈ 𝐵 (3-4)
𝑗 𝑗́ 𝑗
𝑇 −𝑥 ≥ 0 ∀𝑖̈ ∈ 𝐿 (3-5)
𝑘,1 𝑖̈ 𝑜𝑝,𝑘
𝑇 −𝑦 ≥ 0 ∀𝑖̈ ∈ 𝐿 (3-6)
𝑘,2 𝑗̈ 𝑢𝑔,𝑘
∑2 𝑇 +𝐻 ≤ 1 ∀ 𝑘 (3-7)
𝑚=1 𝑘,𝑚 𝑘
ℓ∙𝑇 +∑𝑘 𝐻 ≥ ℓ ∀ 𝑘 (3-8)
𝑘,1 𝑘̇=0 1+𝑘́
ℓ∙𝑇 −∑ℓ 𝐻 ≤ 0 (3-9)
ℓ+1,2 𝑘̇=1 𝑘́
𝑥 , 𝑦 , 𝑇 , 𝐻 ∈ {0,1} ∀ 𝑖𝑗𝑘𝑚 (3-10)
𝑖 𝑗 𝑘,𝑚 𝑘
This model has an objective function to maximize the undiscounted value of the
mine project from both open-pit and underground mine operations as shown in the
Equation (3-2).
Constraint (3-3) is established to maintain a stable pit-wall slope for geotechnical
safety purposes as well as to satisfy the precedence relationship. It makes sure that
all the overlying blocks above a given block are removed prior to mining the block.
The constant, A, is used to represent the number of blocks required to be extracted
to gain access to a given block.
Constraint (3-4) makes sure that there are no overlapping stopes in the ultimate
stope layout. Hence, with all the possible stope layouts which share one or more
common blocks, only one of them can be removed and become part of the final
underground mining layout. The aim is to hold the practicality of the mining
strategy such that none of the stopes or blocks are being evaluated twice in the
outcome.
Constraints (3-5) and (3-6) ensure that only one mining method can be selected
to mine each level. The structure of these constraints is such that one stope or one
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block of a given level is mined through a selected mining method, the entire level
is then considered to be mined by the same mining method. For instance, in Figure
3-2, Block 5 located at level 2 is extracted by open-pit mining, the whole level can
only be mined through open-pit mining and vice versa. Additionally, the level can
be left as a crown pillar if necessary.
Figure 3-2: Equation 3.4 to Equation 3.6 - Only one mining method for each level
Constraint (3-7) and Constraint (3-8) ensure that a certain thickness of the strata
is required to be retained as a pillar between open-pit and underground mining
operations. It guarantees that the crown pillar is positioned between open-pit and
underground working areas. The number of levels required to be retained is
influenced by the geotechnical conditions and structures of the deposit. A crown
pillar is important for the combination of open-pit and underground mining strategy.
It is employed to control the interaction between the surface and underground mine
operations. It also provides geotechnical stability and prevents some operational
issues such as inrush of water into the underground working area. Thus, a crown
pillar helps to reduce, if not eliminate, the geotechnical and operational problems.
A thicker pillar is required for local rock with poor strength to avoid the subsidence
of the surface.
Constraint (3-9) makes sure that if only underground mining method is the most
profitable mining strategy for the project, the pillar requirement is still satisfied.
This constraint has elevated the model by not only solving the transition problem,
but also providing the guidance toward mining method selection process. The
variables present in the model need to be non-negative and integer.
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𝜇 = set of overlying or precedence blocks for block 𝑖
𝑖
𝛼 = set of stopes that share common blocks with stope 𝑗
𝑗
𝛽 = set of horizontally adjacent stopes to stope 𝑗
𝑗
𝛾 = set of vertically stopes adjacent stopes to stope 𝑗
𝑗
𝛿 = set of overlying stopes over stope 𝑗
𝑗
𝜏 = set of stopes that do not share same extraction level with stope 𝑗
𝑗
𝜉 = set of the levels that is located above level 𝑘
𝑘
𝜈 = set of the level that is located immediate above level 𝑘
𝑘
𝑇 = set of scheduling periods
Parameters
𝐴 = total number of overlying blocks that need to be extracted to mine ore block 𝑖
𝐵𝑡 = the discounted value of block 𝑖 in period or year 𝑡
𝑖
𝑆𝑡 = the discounted value of stope 𝑗 in period or year 𝑡
𝑗
𝑑𝑡 = the discounted development cost in period 𝑡
𝑡𝑙 = time lag between commencement of underground development and
underground mining
Η = total number of levels above level 𝑘
𝑘
𝑅 = total number of levels in the orebody model
𝐶 = total number of levels to be retained as a crown pillar
𝑔 = grade or metal content of material in block 𝑖
𝑖
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𝑔̅ = average grade of material in stope 𝑗
𝑗
𝑞 = quantity of material in block 𝑖
𝑖
𝑞̅ = quantity of ore extracted from block 𝑖
𝑖
𝑞 = quantity of ore extracted from stope 𝑗
𝑗
𝑁 = tonnage of block 𝑖
𝑖
𝑁 = tonnage of stope 𝑗
𝑗
𝑂 ,𝑂 = quantity of ore extracted from block 𝑖 and stope 𝑗
𝑖 𝑗
𝑀 ,𝑀 = mining capacity for open-pit and underground operation per period,
𝑜𝑝 𝑢𝑔
respectively
𝑃 = average processing capacity per period 𝑡 over the planning horizon
𝑡
𝐷 = average development capacity per period 𝑡 for underground operation, i.e.
𝑡
if operation can develop 2 levels per period, then 𝐷 = 2
𝐺,𝐺 = upper and lower bound on required head grade in the mine operation
Decision variables
1; if block 𝑖 is mined in period or year 𝑡 by OP mining
𝑥𝑡 = { ; i.e. 𝑥𝑡 ∈ [0,1]
𝑖 0; otherwise 𝑖
1; if stope 𝑗 is mined in period or year 𝑡 by UG mining
𝑦𝑡 = { ; i.e. 𝑦𝑡 ∈ [0,1]
𝑗 0; otherwise 𝑗
1 for OP mining
1; if level 𝑘 is mined with method 𝑚 in year 𝑡;𝑚 = {
𝑒𝑡 = { 2 for UG mining;
𝑘𝑚
0; otherwise
1; if level 𝑘 is in crown pillar
𝐿 = { ; i.e. 𝐿 ∈ [0,1]
𝑘 0; otherwise 𝑘
1; if UG development commences in period 𝑡
𝑎𝑡 = { ; i.e. 𝑎𝑡 ∈ [0,1]
0; otherwise
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3.4.2 Transition Period Model Formulation
The mathematical formulation to determine the optimal transition point, optimal
transition point and optimal scheduling for combination of open-pit and
underground mining strategy is as follows:
max 𝑧 = ∑ [∑ 𝐵𝑡𝑥𝑡 +∑ 𝑆𝑡𝑦𝑡 −𝐷𝑡𝑎𝑡] (3-11)
𝑡∈𝑇 𝑖∈𝐼 𝑖 𝑖 𝑗∈𝐽 𝑗 𝑗
subject to
𝐴∙𝑥𝑡 −∑ ∑𝑡 𝑥𝑡 ≤ 0; ∀𝑖𝑡 (3-12)
𝑖 𝑖́∈𝜇 𝑖 𝑡=1 𝑖́
∑ 𝑥𝑡 ≤ 1; ∀𝑖 (3-13)
𝑡∈𝑇 𝑖
∑ 𝑦𝑡 +∑ 𝑦𝑡 ≤ 1; ∀𝑗,𝑗́ ∈ 𝛼 ,𝑡 ∈ 𝑇 (3-14)
𝑡 𝑗 𝑡 𝑗́ 𝑗
𝑦𝑡 +∑ 𝑦𝑡 ≤ 1; ∀𝑗𝑡,𝑗̈ ∈ 𝛽 (3-15)
𝑗 𝑗̈ 𝑗̈ 𝑗
𝑦𝑡 +∑ 𝑦𝑡 ≤ 1; ∀𝑗𝑡,⃛𝑗 ∈ 𝛿 (3-16)
𝑗 𝑗⃛ 𝑗⃛ 𝑗
∑ 𝑦𝑡 +∑ ∑ 𝑦𝑡 ≤ 1; ∀𝑗,𝑗̀∈ 𝛾 ,𝑡 ∈ 𝑇 (3-17)
𝑡 𝑗 𝑡 𝑗̀ 𝑗̀ 𝑗
∑ 𝑦𝑡 +∑ 𝑦𝑡 ≤ 1; ∀𝑗,𝑗̃ ∈ 𝜏 ,𝑡 ∈ 𝑇 (3-18)
𝑡 𝑗 𝑗̃ 𝑗̃ 𝑗
𝑒𝑡 −𝑥𝑡 ≥ 0; ∀𝑖𝑘𝑡 (3-19)
𝑘1 𝑖
𝑒𝑡 −𝑦𝑡 ≥ 0; ∀𝑗𝑘𝑡 (3-20)
𝑘1 𝑗
𝑒𝑡 +𝑒𝑡 +𝐿 ≤ 1; ∀𝑘𝑡 (3-21)
𝑘1 𝑘2 𝑘
∑ 𝐶 ∙𝑒𝑡 +𝐿 ≥ 𝐶; ∀𝑘,𝑡 ∈ 𝑇 (3-22)
𝑡 𝑘1 𝑘−1
∑ 𝐿 ≥ 𝐶; ∀ 𝑘 ∈ 𝐾 (3-23)
𝑘 𝑘
∑ ∑𝑡 𝑒𝑡́ −Η 𝑡𝑒𝑡 ≥ 0; ∀𝑡𝑘,𝑘́ ∈ 𝜉 (3-24)
𝑘́ 𝑡́=1 𝑘́1 𝑘 𝑘1 𝑘
𝑒𝑡 −𝑒𝑡+1 ≤ 0; ∀𝑘𝑡 (3-25)
𝑘2 𝑘2
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𝑒𝑡 −𝑒𝑡 −𝐿 ≤ 0; ∀𝑘𝑡 (3-26)
𝜈 𝑘2 𝑘2 𝑘
∑𝑇−𝑡𝑙𝑎𝑡 ≤ 1; ∀𝑡 (3-27)
𝑡=1
∑ 𝑒𝑡+𝑑𝑙 −∑𝑡 𝐷 𝑡̇𝑎𝑡̇ ≤ 0; ∀𝑡,𝑘 ∈ 𝐾 (3-28)
𝑘 𝑘2 𝑡̇=1 𝑡
∑ 𝑥𝑡𝑁 ≤ 𝑀 ; ∀𝑡,𝑖 ∈ 𝐼 (3-29)
𝑖 𝑖 𝑖 𝑜𝑝
∑ 𝑦𝑡𝑁 ≤ 𝑀 ; ∀𝑡,𝑗 ∈ 𝐽 (3-30)
𝑗∈𝐽 𝑗 𝑗 𝑢𝑔
∑ 𝑥𝑡𝑂 ≤ 𝑃 ; ∀𝑡,𝑖 ∈ 𝐼 (3-31)
𝑖∈𝐼 𝑖 𝑖 𝑡
∑ 𝑥𝑡𝑂 (𝑔 −𝐺)+∑ 𝑦𝑡𝑂 (𝑔̅ −𝐺) ≤ 0; ∀𝑡,𝑖 ∈ 𝐼,𝑗 ∈ 𝐽 (3-32)
𝑖∈𝐼 𝑖 𝑖 𝑖 𝑗∈𝐽 𝑗 𝑗 𝑗
∑ 𝑥𝑡𝑂 (𝑔 −𝐺)+∑ 𝑦𝑡𝑂 (𝑔̅ −𝐺) ≥ 0; ∀𝑡,𝑖 ∈ 𝐼,𝑗 ∈ 𝐽 (3-33)
𝑖∈𝐼 𝑖 𝑖 𝑖 𝑗∈𝐽 𝑗 𝑗 𝑗
𝑥𝑡,𝑦𝑡,𝑒𝑡 ,𝐿 ,𝑎𝑡 ∈ {0,1}; ∀𝑡 (3-34)
𝑖 𝑗 𝑘𝑚 𝑘
Objective function (3-11) aims to maximize the NPV of the mining project based
on the three main components. In the objective function (3-11), the first two of the
three components are the discounted block economic value for open-pit and
underground mining, respectively. The last component included in the objective
function is the decisive factor for pre-development capital investment. During the
planning stage for the transition from open-pit to underground, pre-production
capital investment is often ignored in the decision-making process. In fact, the
capital investment may affect the decision of going underground. Thus, the
proposed model includes the required pre-production capital investment as a lump
sum dollar value. This will provide a more accurate and comprehensive result and
guidance.
Constraint (3-12) satisfies the precedence pit slope requirements. The constraint
is to ensure that, to mine an underlying block, all immediate predecessors are to be
mined to successfully retain a required slope angle. In Figure 3-3, for example, all
precedence blocks of Block 5 are extracted prior to or at the same time as Block 5
(T ). This is to ensure the accessibility of Block 5 while it needs to be mined.
5
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Figure 3-3: Precedence relationship
Constraint (3-13) - (3-14) enforce to oblige the reserve constraint for open-pit
and underground mining. Constraint (3-13) guarantees that any blocks mined by
open-pit mining can be mined only once in any period. Constraint (3-14) not only
ensures that each stope can only be extracted only once in any time along the life-
of-mine, but also prevents the overlapping stope formation in underground mining.
Constraint (3-15) satisfies the horizontal stope adjacency requirement. It ensures
while mining a given stope, those adjacent stopes are not sequenced at the same
period. Constraint (3-16) ensures the vertical adjacency constraints are satisfied,
referring to the stopes located directly above or below a given stope are not mined
at the same time. These settings are significant to prevent over-scheduling of
mining activities (such as bogging, drilling, and firing stopes) in an area. Overly
intensified mining schedule in an area within one schedule period may lead to
massive voids and exhaustive interactions.
Figure 3-4: Non-concurrent adjacent stope production sequence example (Little and Topal 2011)
Constraint (3-17) structures the offsetting of the stopes vertically to eliminate the
creation of plane of weakness. There are operational and geotechnical risks
associated with stopes located directly above each other due to the plane of
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the final pit-shell. Constraint (3-23) maintains the required thickness of the crown
pillar for the stability of the underground working area. When considering the
thickness of crown pillar, it is important to take into account the factors that may
affect the integrity of the pillar such as natural pillar deterioration, the water level
in the pit bottom and ground support requirement for the development level closest
to the pillar.
Constraint (3-24) enforces the level-based and top-down dependency for the
open-pit. For example, if a block in a given level needs to be mined, the overlying
levels have to be mined prior to or at the same time as the given level.
Constraint (3-25) satisfies the accessibility of a level in underground mining. In
underground mining, once a level is accessible in a period of time, the entire level
remains accessible until the end of LoM. Constraint (3-25) is designed to contain
this nature. Constraint (3-26) is structured to flex the underground formation
process of the production level as each level can be mined by underground mining
or remained unmined.
Constraints (3-27) - (3-28) are designed for the sequence and dependency for
underground development. Constraint (3-27) restricts underground development in
which 𝑎𝑡 is only initiate once along the LoM. Moreover, in underground mining,
the development capacity will determine the number of additional accessible
production levels in each period. For instance, with the available resources, two
additional levels could be available to access per period. Hence, constraint (3-28)
is used to handle the additional developed level per period.
Constraints (3-29) - (3-30) are formulated to maintain upper bound mining
capacity of both open-pit and underground mining. Constraint (3-30) is known as
underground ore handling capacity which is referred to as the capacity of
underground production fleet. Due to the different nature of underground mine
operations, underground development capacity is accounted separately from the
production fleet.
Constraint (3-31) satisfies the mill capacity. In open-pit mining, the material
movement constitutes ore and waste. The destination of the hauled material is either
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the processing plant or waste dump. On the other hand, in underground mining,
only ore will be hauled from a production level to the surface. As a result, typically,
underground mining capacity is equal to processing capacity.
Constraint (3-32) and (3-33) are structured to reduce grade fluctuations and to
optimize plant operation efficiency. The consistency of head grade is important as
it will directly impact the plant recovery; fluctuation in head grade will lead to a
poor plant performance. Hence, upper and lower bounds of ore feed grade are used
to maintain consistency in the head grade.
Constraint (3-34) retains the non-negativity and integrality of the variables as
appropriate.
3.5 VERIFICATION – TWO-DIMENSIONAL CASE STUDY
The optimization models discussed above were programmed in Microsoft Visual
Studio VB.NET (VB.NET 2015) and the mathematical models were solved using
the IBM CPLEX Solver (IBM CPLEX 2013). To examine the functionality of the
models, the models were tested by using a two-dimensional data set. This test
helped to demonstrate how the models work. This section gives the details on the
verification process which includes the introduction of the hypothetical data set,
solution interpretation and the discussion of the result.
A two-dimensional hypothetical data set with 204 blocks was generated to
demonstrate the validity of the models. The hypothetical deposit with a block size
of 20 x 20m and a stope size of 2 x 2 were created. A crown pillar with a minimum
thickness of 40m (two levels) is required to guarantee geotechnical stability. The
block economic values of both open-pit and underground are calculated and shown
in Figure 3-7 and Figure 3-8, respectively.
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Figure 3-7: Block economic model for open-pit mining
Figure 3-8: Block economic model for underground mining
Numerous mining strategies have been considered to demonstrate the validity of
the Transition Point model (Optimization Model 1) and Transition Period model
(Optimization Model 2) proposed in this research. The strategies considered include:
(i) open-pit mining only, (ii) underground mining only, (iii) conventional transition
approach, (iv) proposed Transition Point model and (iv) proposed Transition Period
model. Strategies (i) and (ii) are using the two proposed models in the research by
relaxing the inputs and constraints in the model. For instance, using Transition Point
Model for strategy (i), the underground constraints and inputs have been relaxed to
considered only open-pit mining; vice versa. The information and result of each of
the considered strategy is presented in the Table 3-1.
In comparison with the single mining method approach (open-pit or
underground), the combination of open-pit and underground mining strategy
approaches generated better value. The table has shown that the proposed
Transition Point model generates the highest return which is $207 whereas open-
pit mining and underground mining only generate $111 and $139, respectively. The
conventional transition approach, however, returns a value of $152. The mining
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layouts for open-pit mining only and underground mining only are demonstrated in
Figure 3-11.
As shown in Figure 3-9, the Transition Point model indicates that levels 1 to 4
should be mined using open-pit mining, retained the two levels below the pit as a
crown pillar and extracted the remaining levels using underground mining.
Therefore, the optimal transition point is 80m. However, the conventional transition
approach only employs underground mining after the UPL is reached, as shown in
Figure 3-12. The conventional transition approach only makes the transition to
underground mining 200m below the surface (transition point is 160m). From the
difference of the values generated by the proposed Transition Point model and
conventional transition approach, it is fair to conclude that the conventional
transition approach has an over-mined final pit which leads to the loss of value for
the transition problem - combination of open-pit and underground mining strategy.
Table 3-1: The comparison of the result generated by each possible strategy
Scenario / Mining Strategy Revenue
Open-pit mining only $111
Underground mining only $139
Conventional transition approach $152
Transition Point Model (Optimization Model 1) $207
Figure 3-9: Mining layout generated by the Transition Point Model
Furthermore, the Transition Period model (Optimization Model 2) in this
research aims to obtain the optimal transition point, optimal transition period and
mine schedule simultaneously. Figure 3-10 demonstrates the mining layout for the
proposed Transition Period model which generated an NPV of $169.8. As the
Transition Period model considers elements such as mining capacities, grade profile,
underground mining sequence practicality and underground development
constraints, the final pit layout generated by the Transition Period model is smaller
than the final pit layout of the Transition Point model. The main reason could be
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3.6 SUMMARY
In summary, mathematical models were developed to solve the transition
problem. Two mathematical models are developed. The Transition Point model
aims to search for the mining layout for the combination of open-pit and
underground mining strategy. This model is formulated to achieve the maximized
undiscounted project value while satisfying a range of restrictions. The constraints
considered in the model are open-pit slope constraints, underground mine design
constraints and reserve constraints. At the same time, crown pillar placement is also
described in the model to ensure that a crown pillar is positioned at the level that
returns the least value.
Moreover, the Transition Period model is established as a result of taking further
views about ‘when to make the transition’ and the cost of development. Hence, the
second mathematical model aims to obtain an optimal transition point and optimal
transition period while the mine schedule is developed with the objective of
maximizing the NPV and minimizing capital costs incurred for making the
transition from open-pit to underground. The constraint settings of the models are
included in the open-pit mining sequence, underground mining sequence,
development rate, crown pillar and reserve constraints.
Lastly, a two-dimensional case study was presented to validate the legitimacy of
the proposed models. The results were verified and showed that the constraints
structured in the models are satisfied. Besides, the results indicated that the
proposed models return higher values than any of the single mining method (open-
pit or underground mining) and conventional transition approach.
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Table 4-1: Economic and operational parameters
Open-pit cut-off grade 1 g/t
Underground cut-off grade 2 g/t
Recovery 90%
Discount Rate 12%
Crown pillar 2 Levels
Underground development rate 4 levels per period
Mining capacity for open-pit – 32,000,000 tonnes per schedule period
Maximum
Mining capacity for underground – 7,424,000 tonnes per schedule period
Maximum
Blocks per stope 8 blocks
Precedence blocks for open-pit 5 blocks
Time period 10
Slope angle 45 degrees
4.2 IMPLEMENTATION AND ANALYSIS
4.2.1 Pre-processing steps
Commonly, to solve the transition problem, an economic block model for both
open-pit mining and underground mining (two block models) are imported into
optimization process. As proposed in Section 3.2, only profitable stopes are
qualified and included in the optimization process to reduce the problem size. The
steps to generate the profitable stopes are as below:
1. The economic block model for the underground block model is generated.
Then, blocks in the economic block model are aggregated using the stope
profile of 2x2x2 blocks. As a result, all possible stopes are identified.
2. The next step is to determine the qualified stopes. Hence, within the possible
stopes pool, the stopes with positive values are selected as the qualified
stopes. All the negative value stopes are eliminated.
The data pre-processing took approximately 45 minutes to generate 326 qualified
stopes obtained. As a result, the stope-based methodology successfully reduced the
binary variables for underground mining to 326 stopes. Without the process of
identifying profitable stopes, the model must consider 7,200 blocks which can
create millions of combinations with a stope profile of 2x2x2. Hence, with the step
of processing, the number of variables required for underground mining has
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reduced significantly. Then, the qualified stopes determined were substituted into
the proposed mathematical models.
Moreover, the size of the problem for proposed Transition Period model increases
exponentially as time is considered in the optimization model. Thus, to further
reduce the problem size of Transition Period model, the UPL is determined prior to
the optimization process. UPL is the largest pit where open-pit can mine and it
generates the highest undiscounted profit returns to the mine operation. Therefore,
while taking underground mining into account, the final pit of the combination of
open-pit and underground mining strategy can be significantly smaller than the UPL
(Fuentes 2004). Therefore, using the UPL for the Transition Period model will not
violate the optimality of the model. As a result of the UPL definition, the variables
for open-pit mining are reduced to 1,366 blocks. The generated UPL is shown in
Figure 4-2. The UPL contains 1,394 blocks which generates the undiscounted
cashflow of $2.362 billion.
Figure 4-2: UPL generated to reduce problem size for the Transition Period model
The two proposed models resulted in two mathematical problems. Each
mathematical problem involves thousands of variables. A standard computer with
a specification of 2.8 GHz CPU and 16 GB RAM was used to solve the
mathematical models. Based on experience, improvement in computational gap of
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1% will take a long time. However, it may not see a significant improvement in the
generated result in comparison to the optimal result. Thus, an appropriate gap can
be utilized to shorten the computation time. In this research, a gap of 5% was used.
4.2.2 Models implementation
The result of applying the Transition Point model is presented in Figure 4-3. The
optimal solution recommends the first six levels (240m) to be mined by open-pit
mining. Then, the Level 7 and 8 are left as a crown pillar. Underground mining is
recommended to extract the remaining ore underneath the crown pillar. The
undiscounted value generated by Transition Point model is $3.740 billion which is
higher than the UPL result ($2.362 billion). Hence, the optimal transition point is
at level six with the transition depth of 240m.
Figure 4-3: Optimal mining layout of the Transition Point model
For the Transition Period model implementation, two scenarios are presented.
The first scenario considers no delay in the production during the transition from
open-pit to underground, meanwhile, the second scenario considers two periods of
delay in the production. In some cases, the mine operation is unable to make the
smooth transition from open-pit to underground mining for various reasons such as
the interaction between open-pit mining activities and underground portal
development as well as time to arrange different mining equipment and personnel
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required for the transition to underground. Hence, second scenario demonstrated
the possibilities of accommodating delays in the production during the transition
from open-pit mining to underground mining by applying the Transition Period
model.
For the first scenarios, with no delay in production during the transition from
open-pit mining to underground mining, the result is shown in Figure 4-4. The
optimized discounted value is $2.601 billion. The model suggested to extract the
first eight levels (320m) by open-pit mining. A crown pillar is recommended to be
placed at Level 9 and 10. Underground mining method will be adopted to extract
the remaining reserve underneath the crown pillar. Hence, the optimal transition
point and transition period is 320m and Period 3, respectively. Underground mining
will start at Period 4.
Figure 4-4: Scenario 1 Transition Period model result - with no delay
For the second scenario in which the Transition Period model is implemented
with a two-period delay in production during the transition from open-pit to
underground mining, the result is shown in Figure 4-5. The generated discounted
value is $2.507 billion. The transition period and point are the same as the result of
not having any delay period. The main difference between the two scenarios is that
underground mining is scheduled to start at Period 6 instead of immediately after
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layout and optimal mine schedule for the combination of open-pit and underground
mining strategy, it is more computationally demanding in comparison to the
Transition Point model. The number of variables, number of constraints and
solution time are summarized as shown in Table 4. The table indicates that the
growth of model complexity and increase of number of variables can affect the
solution time exponentially. This is also one of the main reasons why in the mining
industry, oftentimes, the pit optimization process and extraction period optimization
process are treated independently. Despite that, the independency of those two
processes are unable to produce optimal results. Hence, the Transition Point model
creates value for the cases which are required to perform a brief evaluation for a
combination of open-pit and underground mining strategy.
Table 4-3: Mathematical model size and solution time
Transition Transition
Descriptions
Point model Period model
Number of open-pit variables (blocks) 7,200 50,400
Number of underground variables (stopes) 326 2,282
Other variables 54 424
Total Constraints 30,898 193,998
Solution time (seconds) 10,213 44,679
4.3 CHALLENGES OF IMPLEMENTATION
From the implementation, it is evident that the mathematical models can solve
the transition problem optimally. However, the foremost challenge of
implementation of the models in a large/real dataset is the large-scale issue. The
larger the scale of the problem, the higher the computation time. Hence, the large-
scale problem is less likely to be solved within the reasonable time using a standard
computer. To demonstrate the bottleneck of the model implementation, a range of
instances of the problem have been solved and the result is shown in Table 5.
From the summary presented in Table 5, although, the practicality of the models
proposed in this research project is valid and genuine and the problem of size
reduction strategies have been adopted, it is still flawed. Thus, the large-scale issue
for open-pit mining needs to be emphasized.
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As mentioned in the literature (Section 2.2.1), open-pit mine planning and the
optimization problem are computationally intractable due to their large-scale nature.
Hence, reducing the number of binary integers in the LP model is the most
important subject in this matter. The clustering or block aggregation technique is
one of the available techniques to handle the large-scale problem. The clustering
technique aims to aggregate blocks which have similar properties such as location,
rock type, grade, and others. By aggregating blocks, a group of blocks can be
represented as one entity, hence, reducing the number of binary variables in the LP
model.
Table 4-4: Iterations summary
Transition Point Transition Point Transition Transition
Model: Model: Period Period Model:
No. of Decision Solution Time Model: Solution Time
Variables (seconds) No. of (seconds)
Variables
962 443 9,638 616
3,059 867 30,616 1,298
5,396 4,218 53,992 5,113
10,046 4,694 100,500 7,455
14,896 6,660 149,006 33,090
25,092 9,081 250,974 45,575
30,640 10,020 306,458 78,913
42,760 10,812 427,664 > 4 days
No solution
4.4 SUMMARY
This chapter has demonstrated the three-dimensional implementation for the two
exact optimizations - Transition Point model and Transition Period model. From
the series of results presented in this chapter, for the deposit which has potential to
make the transition from open-pit to underground mining required underground
mining to be considered as a viable mining strategy in the beginning of the planning
and optimization processes. If the planning process is partial towards any mining
method, it will impact the project value significantly. For instance, the stand-alone
open-pit operation generates an undiscounted value of $2.362 billion. Meanwhile
extending the optimization process to consider both open-pit and underground
mining concurrently, the project generates a discounted value of $3.740 billion.
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5.1 BACKGROUND
The main challenge of the MILP models to solve the transition from open-pit to
underground mining problem is their nature of having a huge number of binary
decision variables. The increased number of variables leads to the exponential
increase in computational time of the model. Moreover, the growing number of
variables also increases the complexity of the model when considering the mining
period - Transition Period model. During underground mining modelling process,
a stope-based methodology is presented to aggregate the blocks into a mineable
stope and it includes positive value stopes in the model implementation only in
order to decrease the number of variables (Section 3.2). To further reduce the
number of binary variables, the agglomerative hierarchical cluster analysis is
employed to reduce the size of the problem of the open-pit model.
The agglomerative hierarchical cluster analysis is a bottom-up aggregation
method. It considers each block or component as a cluster. The method starts with
constructing a similarity matrix for all data points. Then, the aggregation starts from
the most similar two clusters/blocks and make the way up to reach the desired
number of clusters (Aggarwal 2014; Jain and Dubes 1988; Bailey 1975).
There are several agglomerative clustering methods such as single link, complete
link, average, centroid, etc. Among these methods, the single link and complete link
are the most commonly used methods. The single link hierarchical clustering
method emphasizes mostly similar clusters. Hence, this method opts for the regions
where clusters are closest. Due to this characteristic, this method is defined as local
similarity-based method and capable to efficiently cluster different shapes of data
objects such as non-elliptical and elongated shaped groups. On the other hand, the
complete link hierarchical clustering method stresses on the dissimilarity of clusters.
In other words, the cluster pairs with the least dissimilarity index will be merged.
This behavior is considered as non-local similarity based method (Aggarwal 2014).
For mining applications, the most significant aspect for hierarchical clustering is
the geospatial domain. The agglomerated clusters are required to be located in the
same region due to practicality reasons. Hence, single link method is employed due
to its suitability.
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𝜇 = A numerical factor assigned for localized neighborhoods
𝜔 = A numerical penalty factor assigned for non-localized neighborhoods
𝛿 = A numerical factor assigned to not maintaining the slope requirement
𝜃 = A numerical penalty factor assigned to not maintaining the slope
requirement
𝛽 = A numerical factor assigned for blocks that share the same level
𝜏 = A numerical penalty factor for blocks that do not share the same level
5.2.2 Formulation
A similarity index is used to construct similarity matrix before block aggregation
is exercised. In this research, the proposed similarity index calculation for cluster
analysis is given by Equation 5-1:
𝑆 = 𝐷 ×𝑁 ×𝐺 ×𝑆𝐹 ×𝐿 (5-1)
𝑖𝑗 𝑖𝑗 𝑖𝑗 𝑖𝑗 𝑖𝑗 𝑖𝑗
• Distance factor: This factor is to ensure that each cluster only consists of blocks
that are close to each other. The distance factor for two blocks (block 𝑖 and 𝑗) is
calculated using the Euclidean distance method as shown in Equation (5-2).
𝐷 = √(𝑥 −𝑥 )2+(𝑦 −𝑦 )2 +(𝑧 −𝑧 )2 (5-2)
𝑖𝑗 𝑗 𝑖 𝑗 𝑖 𝑗 𝑖
• Neighborhood factor: The neighborhood factor is used to reinforce the
localization of those aggregated blocks. A profile or an envelope needs to be
defined as a boundary of a neighborhood. Then, all the blocks located inside
the profile will be assigned a factor (𝜇) and those blocks sited outside the
boundary will be penalized by a given penalty factor (𝜔). In the example shown
in Figure 5-1, a profile of 3 by 3 blocks is employed. By using the neighborhood
profile, the neighborhood members of Block 6 are 𝐵𝑙𝑜𝑐𝑘 6 =
{1,2,3,5,7,9,10,11}. Hence, the neighborhood factor between Block 6 and
each of the neighborhood members is 𝜇.
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𝜇,if block 𝑗 is within the neighbourhood profile of block 𝑖
𝑁 = { (5-3)
𝑖𝑗 𝜔,otherwise
Figure 5-1: Neighborhood factor schematic
• Grade factor: This factor is to control the grade deviation of blocks within a
cluster which is considered in production scheduling optimization as shown in
Equation (5-4).
𝐺 = (𝑔 −𝑔 )2 (5-4)
𝑖𝑗 𝑖 𝑗
• Slope factor: This factor is assigned a penalty factor to those blocks that are
located outside the slope requirement. 𝛿 is factor assigned to those blocks that
are member of the blocks required to maintain the slope stability of a given
block; 𝛿 should be a value greater than 0 and less than 1. A value of 𝜔 is
assigned to those blocks which are not a member of the blocks required to
maintain the slope requirement; 𝜃 should be a value greater than or equal to 1.
For example, in Figure 5-2, the slope factor between Block 2 and Block 5 is 𝛿;
whereas, slope factor between Block 4 and Block 5 is 𝜃 as these are not
members of required to maintain slope requirement between each other.
𝛿,if block 𝑗 can help to maintain a slope stability of block 𝑖
𝑆𝐹 = { (5-5)
𝑖𝑗 𝜃,otherwise
Figure 5-2: Example for slope penalty factor
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• Level factor: This factor is designed to penalize those blocks which are not
located on the same level as a given block. 𝛽 is assigned to those blocks that
share the same level as a given block; 𝛽 should be a value greater than 0 and
less than 1; 𝛽 = (0,1). Whereas 𝜏 is allocated to those blocks not sharing the
same level as a given block; 𝜏 should be a value greater than or equal to 1. For
instance, using Figure 5-2 as an example, Blocks 4 and 5 are located on the
same level (Level 2). Hence, 𝐿 is assigned 𝛽. On the other hand, 𝐿 is
45 25
assigned 𝜏 as block 2 and 5 are located on level 1 and 2 respectively.
𝛽,if block 𝑗 is located on the same level as block 𝑖
𝐿 = { (5-6)
𝑖𝑗 𝜏,otherwise
Conceptually, if the combination of open-pit and underground mining strategy
is employed, the final pit should be smaller than ultimate pit limit. Therefore, in the
process of performing cluster analysis, only blocks within the ultimate pit are
considered. Besides, the main reason for generating the ultimate pit limit before
implementing the hierarchical clustering algorithm is to control any over-clustering.
Over-clustering can happen when blocks in an area are very similar to each other.
Waste blocks are good examples of this over-cluster effect. For instance, if there is
no ultimate pit limit boundary for the clustering algorithm to run, waste blocks can
cluster together as a big cluster group due to their similarity. Hence, this behavior
can lead to an over-mined or under-mined clustering effect.
The process of performing cluster analysis is shown in Figure 5-3.
Figure 5-3: Process for Cluster Analysis
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The third step presented in the cluster analysis process is as follows:
• Compute the similarity index of the blocks within the pit limit. The
similarity index is presented in a matrix form and is shown in Figure 5-4.
• Run the hierarchical cluster analysis on Matlab (MATLAB R2015b) by
using the similarity index formulation proposed in the research.
The process of clustering data has two most common types of methods which
can be utilized to define the number of clusters. They are the natural division
method and specifying arbitrary cluster method. The first method divides the
dataset into discrete clusters using a ‘threshold’ value. This method allows the
system to determine the natural partitions of the dataset. In this method, an
inconsistency coefficient is normally used to verify the dissimilarity of clusters and
inconsistent links between clusters. This method utilized the inconsistency
coefficient function to create clusters. Hence, the inconsistent link plays a
significant part in the process of determination of the natural division in a set of
data. The second method which is the specifying arbitrary cluster method is
relatively simple and straightforward. Basically, this method allows the user to
determine the number of clusters and cluster data based on the height between two
nodes in the cluster tree. This method is dependent on the user experience. Hence,
it is difficult for a user to determine the correct number of clusters for the dataset.
Whereas, due to the nature of the first methodology as explained, the clusters group
created by this method is more appropriate for this research.
Figure 5-4: Sample of matrix generated by the similarity index computational process
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5.3 VERIFICATION – TWO-DIMENSIONAL CASE STUDY
The two-dimensional case study shown in Section 3.5 was used for the
verification process and the results were compared. As discussed earlier, the
hierarchical cluster analysis is proposed to handle the computational complexity of
the MILP model. The ultimate pit has been generated as shown in Figure 5-5. Then,
the blocks within the ultimate pit are included in the cluster analysis process. All
the details such as the location of the block, precedence blocks, block value and
grade are tabulated into the cluster analysis model as shown in Table 6. These
details are used to calculate the similarity index between blocks using the formula
presented in Section 5.2. The computed similarity index is used to perform the
hierarchical cluster analysis. The result generated is demonstrated in Figure 5-6. In
Figure 5-6, each block has been assigned to a cluster attribute. Hence, blocks which
share the same attributes belong to the same cluster. The cluster sets are substituted
into the proposed model. The result generated by both the Transition Point Model
and Transition Period Model is shown in Figure 5-7.
Table 5-1: Example of details or attributes required to perform cluster analysis
Block Location Grade Block value Precedence blocks
1 X1 , Y1 Grade (Block 1) 1 NIL
. . . . .
. . . . .
. . . . .
20 X2 , Y3 Grade (Block 20) -3 Blocks{2,3,4}
. . . . .
. . . . .
. . . . .
128 X9 , Y8 Grade (Block 128) 2 Blocks{110,111,112}
Figure 5-5: Cluster analysis result – cluster group
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analysis) is period 3, whereas the transition period post-cluster analysis is period 4.
Due to the alteration in transition period post-cluster analysis, the mining layout
and sequence for underground mining have been affected. Although there are some
minor effects in post-cluster analysis in term of final pit layout, mining sequencing
and transition period, the difference in NPV generated is minimal which is
approximately 2%.
Table 5-2: Post-cluster Analysis results – two-dimensional case study
Scenario / Mining Strategy Revenue
Transition Point Model $207
Transition Period Model $167
Figure 5-8: Over-mined due to clustering effect
5.4 SUMMARY
In summary, the main challenge of MILP model is the increase number of
decision variables will boost the solution time exponentially. In this research,
therefore, hierarchical clustering algorithm is employed to handle the computation
complexity of the mine planning and optimization in open-pit mining. A new
similarity index formulation is proposed to construct the similarity index for block
aggregation purposes. The proposed similarity index is constructed by considering
geospatial requirements along with grade factor and slope factor. The proposed
hierarchical clustering algorithm is to be implemented within the ultimate pit limit.
Once the block aggregation result is generated, it can be substituted into the
proposed models in section 3 to generate the optimal transition point and period. A
two-dimensional case study is presented to demonstrate the validity of the proposed
methodology and comparisons of the results.
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Table 6-1: Scheduling parameters
Open-pit cut-off grade 1 g/t
Underground cut-off grade 2 g/t
Recovery 90%
Discount Rate 12%
Crown pillar 2 Levels
Underground development rate 8 levels per period
Mining capacity for open-pit – 150 million tonnes per scheduling period
Maximum
Mining capacity for underground – 37 million tonnes per scheduling period
Maximum
Blocks per stope 8 blocks
Precedence blocks for open-pit 5 blocks
Schedule period 7
Slope angle 45 degrees
6.2 HIERARCHICAL CLUSTERING ALGORITHM
As mentioned in the literature section, while considering underground mining as
a viable option in the initial mine planning and optimization processes, the final pit
is likely to be smaller than the UPL generated by a stand-alone open-pit case
scenario. The ultimate pit limit consists of 13,555 blocks which are shown in Figure
6-2. The UPL ends at level 19 which is at 460m. Figure 6-2 displays the UPL
generated for the hierarchical clustering algorithm.
Then, those blocks within the ultimate pit limit are substituted into the
hierarchical clustering algorithm as shown in Section 5.2. The result from the
hierarchical clustering algorithm successfully reduced the size of the open-pit
mining from 13,555 blocks into 1,507 clusters which is approximately 85% of
reduction in size of the problem. In the result generated by the hierarchical
clustering algorithm, the maximum number of blocks in a cluster group is 39 blocks.
Table 9 tabulates the count of the number of blocks within the each of the first 30
cluster groups. For example, in Table 9, each of Clusters 1 to 4 consists 3 blocks
and Cluster 7 contains 6 blocks. Table 10 presents the example of the list of the
blocks within the first seven set of the cluster group. In Table 10, the three blocks
contained in Cluster 1 (as mentioned in Table 9) are X22Y22Z37, X22Y23Z37 and
X22Y24Z37. Overall, the clustering algorithm used 8,936 seconds to solve the
clustering problem.
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6.3 OPTIMIZATION MODELS
The output from the clustering algorithm is substituted into the proposed optimization
models as an open-pit mining input. Besides, the underground mining input has been
proposed by using the stope-based methodology. Hence, the input for underground
mining reduced to 2,136 positive stopes from 83,025 blocks. This process took 12 hours
and 16 minutes to be completed. The larger the block model, the more the combination
of stopes required, hence, it requires much longer time to process and define all the
profitable stopes.
The number of variables and constraints required for both optimization models are
shown in Table 11. For the Transition Point Model which only considers the optimal
transition point, it consists of approximately 292,000 constraints and a total of
approximate 4,000 binary variables. The Transition Point Model takes approximately 83
seconds to solve. On the other hand, the Transition Period Model which considers both
optimal transition point and period require approximately 1.8 million and 32,000 as
number of constraints and variables, respectively. As the scale of the problem increases
drastically compared to the Transition Point Model, the Transition Period Model uses
approximately 30 hours to generate a result with the gap of 4.9%. Both models were
solved on a standard computer with a specification of 2.8 GHz CPU and 16 GB RAM.
Table 6-4: Number of variables and constraints for large-scale implementation
Transition Point Transition
Descriptions
Model Period Model
Number of open-pit variables 1,507 15,049
(clusters)
Number of underground 2,136 14,952
variables (stopes)
Other variables 123 1,435
Total Constraints 291,952 1,790,891
Solution time (seconds) 83 93,463
The result of the Transition Point Model is presented in both Figure 6-3 and Table 12.
Figure 6-3 illustrates the optimal layout of the transition problem and Table 12 shows the
mining method selection by level. The result for Transition Point Model recommends
ceasing open-pit mining at level 24 which is at a depth of 360m and leave Levels 22-23
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as a crown pillar. Underground mining method is suggested to start from Level 21 and
below. From the result generated by Transition Point Model, 13,390 blocks are to be
mined by open-pit mining and 112 stopes are to be mined by underground mining. The
undiscounted cashflow generated by Model 1 was $191.02 million.
Figure 6-3: Transition Point Model result of large-scale implementation
The result of the Transition Period Model is shown in Figure 6-4 and Table 13. In
Table 13, the result suggests mining the first 20 levels by open-pit mining which is up to
400m deep and mine Level 19 and below by underground mining. The two levels below
the final pit are left as a crown pillar. The NPV generated by the Transition Period Model
is $145.71 million. The material movement by period generates by the Transition Period
Model is shown in Table 14. The total material movement for the entire schedule periods
is approximately 309 million tonnes with the split of ore and waste of approximately 92
million tonnes and 217 million tonnes, respectively.
The results proved that, by using the hierarchical clustering algorithm, the proposed
Transition Point Model and Transition Period Model are able to be implemented in a
larger dataset. Therefore, the main challenge discussed in Section 4.3 which is the large-
scale issue can be eased by using the proposed hierarchical clustering algorithm.
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