# Which one of the following is not a casual forecasting method?

2. Econometric models
3. Linear regression
4. Multiple regression

Option 1 : Trend adjusted exponential smoothing

## Exponential Smoothing Method MCQ Question 1 Detailed Solution

Explanation:

• Forecasting is the prediction of future sells or demand of the particular product.
• It is a projection based upon past data and art of human judgement.

Types of forecasting method

 Qualitative or Subjective Quantitative or Objective Judgemental Opinion Survey Market trial Market research Delphi technique Time series Past average Moving average Weighted moving average Experimental smoothing Casual or Econometrics Correlation Regression Used for long-range and new product Used for Short-range and for old products

# Which of the following is a technique used for forecasting?

1. PERT/CPM
2. Exponential smoothing
3. Gantt Chart
4. Control Chart

Option 2 : Exponential smoothing

## Exponential Smoothing Method MCQ Question 2 Detailed Solution

Explanation:

Forecasting

• Forecasting is defined as estimating the future value that a parameter will take. Most scientific forecasting methods forecast the future value using past data.
• Some simple forecasting models using time series data are simple average, moving average and simple exponential smoothing.

Moving average Method or rolling average Method:

• In this method, fresh average is calculated at the end of each period by adding the actual demand data for the most recent period and deleting the data for the order period. It gives equal weight to each of the most recent observations.

$${F_{n+1}} = \frac{{{D_1} + {D_2} + {D_3} + {D_4} + \ldots \ldots \ldots \ldots \ldots \ldots + {D_n}}}{n}$$

Weighted moving average Method:

• This method gives unequal weight to each demand data with more weight to recent data.

$${F_{n+1}} = \left[ {{w_{1}} \times {D_{1}} +{w_{2}\times {D_{2}}} +..........+ {w_{n}} \times {D_{n}}} \right]$$

Exponential Smoothing Method:

• This method gives weight to all the previous data and the pattern of weight assigned is exponentially decreasing in order with most recent data is given the highest weight.
• In exponential smoothing method of forecast, the forecast for the next period is equal to

F= α Dt-1 + (1 - α) Ft-1

where, Dt-1 = latest figure sale or latest demand,  Ft-1 = old forecast, α = exponential smoothing constant

Project

• A project may be defined as a combination of interrelated activities which must be executed in a certain order before the entire task can be completed.
• The aim of planning is to develop a sequence of activities of the project so that the project completion time and cost are properly balanced.
• To meet the objective of systematic planning, the management has evolved several techniques applying network strategy.
• PERT (Programme Evaluation and Review Technique) and CPM (Critical Path Method) are network techniques which have been widely used for planning, scheduling and controlling the large and complex projects.

Difference between PERT and CPM (Critical Path Method)

 PERT CPM 1. Probabilistic approach 1. Deterministic approach 2. Three-time estimate 2. One - time estimate 3. Event oriented network model 3. Activity-oriented network model 4. The slack concept is used 4. Float concept is used 5. Project crashing is not possible 5. Project crashing is possible 6. Deals with probabilistic time estimates 6. Deals with deterministic time estimates

Gantt charts:

• Gantt charts are mainly used to allocate resources to activities.
• The resources allocated to activities include staff, hardware, and software.
• Gantt charts are useful for resource planning. A Gantt chart is a special type of bar chart where each bar represents an activity.
• The bars are drawn along a timeline.
• The length of each bar is proportional to the duration of time planned for the corresponding activity.

Control charts:

• Control chart is a graphical representation of the collected information.
• It indicates whether a process is in control or out of control.
• It determines process variability and detects unusual variations taking place in a process.
• It ensures product quality level.
• It provides information about the selection and setting of tolerance limits.

# In exponential smoothening method, which one of the following is true?

1. 0 ≤ α ≤ 1 and high value of α is used for stable demand
2. 0 ≤ α ≤ 1 and high value of α is used for unstable demand
3. α ≥ 1 and high value of α is used for stable demand
4. α ≤ 0 and high value of α is used for unstable demand

Option 2 : 0 ≤ α ≤ 1 and high value of α is used for unstable demand

## Exponential Smoothing Method MCQ Question 3 Detailed Solution

Concept:

The general form of forecasting is Ft = Ft-1 + α. (Dt-1 – Ft-1)

where α = smoothing constant and its range is 0 ≤ α ≤ 1

For Immediate forecast → high value of "α" is high and less for other forecasts.

Hence the high value of forecast is only chosen when the nature of demand is not reliable rather unstable.

$$α = \frac{2}{{n + 1}}$$

where, n = no. of period of moving average, Ft = recent forecast, Ft-1 = previous forecast, Dt-1 = previous demand

• If α = 0, then Ft = Ft-1 ……….…..(limit of stability)
• If α = 1 then Ft = Dt-1…………….(limit of responsiveness)​

​

​

# Which of the following forecasting methods takes a fraction of forecast error into account for the next period forecast?

1. simple average method
2. moving average method
3. weighted moving average method
4. exponential smoothening method

Option 4 : exponential smoothening method

## Exponential Smoothing Method MCQ Question 4 Detailed Solution

Explanation:

Forecast error (ei) for a period is defined as the difference between actual and actual and forecasted demand.

ei = Actual demand - Forecast demand ⇒ Di - Fi

Exponential forecasting:

$${F_T} = {F_{T - 1}} + α ({D_{T - 1}} - {F_{T - 1}})$$

where

FT is the forecast for the next period

$$({D_{T - 1}} - {F_{T - 1}})$$ is the forecast error and

α is the smoothing constant.

Thus exponential smoothing takes into account the forecast error of the previous period, for the forecast of the next period.

Simple Average Method:

In the simple moving average, we take the average of the past data points for future demand.

For 'n' period moving average forecast will be given by:

$${F_{n+1}} = \frac{{{D_1}\;+\;{D_2}\;+\;{D_3}\;+ \;{D_4}\;+\;\ldots \ldots \ldots \ldots \ldots \ldots \;+\;{D_n}}}{n}$$

Weighted Moving Average Method:

In weighted moving average, the highest weightage is given to recent data & it decreases for older data points.

For n period weighted moving average, weightage is as follows:

$$\frac{n}{{{\rm{\Sigma }}n}},\;\frac{{n - 1}}{{{\rm{\Sigma }}n}},\;\frac{{n - 2}}{{{\rm{\Sigma }}n}}, \;- - - - - - - ,\frac{1}{{{\rm{\Sigma }}n}}$$

$${F_{n+1}} = \left[ ({{w_{1}} \times {D_{1}})\;+\;({w_{2}\times {D_{2}}})\;+\;..........+\;({w_{n}} \times {D_{n}}})\right]$$

# The current period forecast becomes equal to last period forecast for the value of smoothing constant equal to

1. 1
2. 2
3. 0
4. 0.5

Option 3 : 0

## Exponential Smoothing Method MCQ Question 5 Detailed Solution

Explanation:

Forecast value in Smoothing constant method is given by-

Ft = Ft-1 + α [ Dt-1 - Ft-1 ]

where Ft = Current period forecast, Ft-1 = last period forecast, Dt-1 = last period demand, α = smoothing constant

for α = 0

Ft = Ft-1

Hence for α = 0 only the current period forcast becomes equal to last period forecast.

Important Points

For α = 1 current period forecast will become equal to the last period demand.

# The sale of cycles in a shop in four consecutive months are given as 70, 68, 82, 95. Exponentially smoothing average method with a smoothing factor of 0.4 is used in forecasting. The expected number of sales in the next month is

1. 59
2. 73
3. 86
4. 136

Option 3 : 86

## Exponential Smoothing Method MCQ Question 6 Detailed Solution

Concept:

When only demand/sales are given from previous data, then forecast for the next month:

$$F_t=F_{t-1}+\alpha(D_{t-1}-F_{t-1})$$

ft = forecast of next month,

ft-1 = forecast for the previous month and so on.

Dt-1 = Demand of the previous month

Calculation:

Given:

 Month Dt Ft 1 70 70 2 68 3 82 4 95

$$F_t=F_{t-1}+\alpha(D_{t-1}-F_{t-1})$$

$$F_2=F_{1}+\alpha(D_{1}-F_{1})$$

$$F_2=70+0.4 \times (70-70)$$

F2 = 70

$$F_3=F_{2}+\alpha(D_{2}-F_{2})$$

$$F_3=70+0.4 \times (68-70)$$

F3 = 69.2

$$F_4=F_{3}+\alpha(D_{3}-F_{3})$$

$$F_4=69.2+0.4 \times (82-69.2)$$

F4 = 74.32

$$F_5=F_{4}+\alpha(D_{4}-F_{4})$$

$$F_5=74.32+0.4 \times (95-74.32)$$

F5 = 82.59

Note: In the options, 82.59 is not available so always select the higher number from the given answer.

# For a canteen, the actual demand for disposable cups was 500 units in January and 600 units in February. The forecast for the month of January was 400 units. The forecast for the month of March considering smoothing coefficient as 0.75 is _______.

## Exponential Smoothing Method MCQ Question 7 Detailed Solution

Concept:

𝐹𝑡+1 = 𝛼𝐷𝑡 + (1 − 𝛼) 𝐹𝑡 = 𝐹𝑡 + α (Dt - Ft)

This equation can be used when simple exponential smoothing is used as a forecasting model.

Here Ft represents the forecast for period t, Dt is the known demand for period t and α is the smoothing constant.

Calculation:

Forecaster for February:

F2 = 400 + 0.75 (500 – 400) = 475

Forecaster for March:

F3 = 475 + 0.75 (600 – 475) = 568.75

# In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to

1. -1
2. zero
3. 0.5
4. 1

Option 4 : 1

## Exponential Smoothing Method MCQ Question 8 Detailed Solution

Explanation:

In exponential smoothing method of forecast the forecast for the next period is equal to

Ft = α Dt-1 + (1 - α) Ft-1

If we further expand the expression

Ft = α Dt-1 + (1 - α) (α Dt-2 + (1-α) Ft-2

F= α Dt-1 + α (1-α ) Dt-2 + (1 - α )2 Ft-2

If we put the value of α = 0.8 (Close to 1) then,

Ft = 0.8 Dt-1 + 0.16 Dt-2 + 0.04 Ft-2

It can be observed from the above expression that recent data is given more weightage compared to the previous data, therefore, the higher value of exponential smoothing constant (Close to 1) is used for changing pattern of demand or to follow recent demand.

# If the actual demand of a product is 62, a previous year's forecast is 57, and the value of smoothing constant is 0.3, what would be the forecast for the current year using exponential smoothing method of forecasting?

1. 58.5
2. 60
3. 62.5
4. 65

Option 1 : 58.5

## Exponential Smoothing Method MCQ Question 9 Detailed Solution

Concept:

For exponential smoothing method,

$$F_t = F_{t-1} + α (D_{t-1} – F_{t-1})$$

where Ft-1 = previous year's forecast, Ft  = current year's forecast, Dt-1 = previous year's demand, α = smoothing constant

Calculation:

Given:

Ft-1 =  57, Dt-1 = 62, α = 0.3

$$F_t = F_{t-1} + α (D_{t-1} – F_{t-1})$$

$$\Rightarrow F_{t}= 57+ 0.3\times (62 – 57)$$

t  = 58.5.

# In forecasting by exponential smoothing, if α is a smoothing constant, then:

1. New Forecast = α (latest sales figure) + (1 - α ) (old forecast)
2. New Forecast = α (latest sales figure) – (1 - α) (old forecast)
3. New forecast = α (latest sales figure) + (1 + α) (old forecast)
4. New Forecast = α (latest sales figure) – (1 + α) (old forecast)

Option 1 : New Forecast = α (latest sales figure) + (1 - α ) (old forecast)

## Exponential Smoothing Method MCQ Question 10 Detailed Solution

Explanation:

• Forecasting is defined as estimating the future value that a parameter will take. Most scientific forecasting methods forecast the future value using past data.
• Some simple forecasting models using time series data are simple average, moving average and simple exponential smoothing.

Moving average Method: or rolling average Method:

• In this method, fresh average is calculated at the end of each period by adding the actual demand data for the most recent period and deleting the data for the order period. It gives equal weight to each of the most recent observations.
• $${F_{n+1}} = \frac{{{D_1} + {D_2} + {D_3} + {D_4} + \ldots \ldots \ldots \ldots \ldots \ldots + {D_n}}}{n}$$

Weighted moving average Method:

• This method gives unequal weight to each demand data with more weight to recent data.
• $${F_{n+1}} = \left[ {{w_{1}} \times {D_{1}} +{w_{2}\times {D_{2}}} +..........+ {w_{n}} \times {D_{n}}} \right]$$

Exponential Smoothing Method:

• This method gives weight to all the previous data and the pattern of weight assigned is exponentially decreasing in order with most recent data is given the highest weight.
• In exponential smoothing method of forecast, the forecast for the next period is equal to
• Ft = α Dt-1 + (1 - α) Ft-1
• where, Dt-1 = latest figure sale or latest demand,  Ft-1 = old forecast
• If we further expand the expression
• Ft = α Dt-1 + (1 - α) (α Dt-2 + (1-α) Ft-2
• F= α Dt-1 + α (1-α ) Dt-2 + (1 - α )2 Ft-2
• If smoothing coefficient (α) is 1 then the latest forecast would be equal to the previous period actual demand.
• The technique is not as simple as compared to the moving average method.
• All observations are not assigned equal weightage

# For a product, the forecast and the actual sales for December 2008 were 25 and 20 respectively. If the exponential smoothing constant (α) is taken as 0.2, the forecast sales for January 2009 would be.

1. 21
2. 23
3. 24
4. 27

Option 3 : 24

## Exponential Smoothing Method MCQ Question 11 Detailed Solution

Concept:

By the exponential smoothing method:

$${F_t} = {F_{t - 1}} + α \left[ {{D_{t - 1}} - {F_{t - 1}}} \right]$$

where Ft = forecast for the period t, Ft-1 = Forecasted demand for the last period, Dt-1 = Demand for the last period, α = exponential smoothing constant

Calculation:

Given:

Ft-1 = 25, Dt-1 = 20, α = 0.2

∴ By using the formula by exponential smoothing factor, we have

$${F_t} = {F_{t - 1}} + α \left[ {{D_{t - 1}} - {F_{t - 1}}} \right]$$

Fjan (2009) = FDec + α (DDec - FDec)

Fjan (2009) = 25 + 0.2(20 - 25)

Fjan (2009) = 25 - 1 = 24

# Which one of the following forecasting models best predicts the turning point?

1. Simple exponential smoothing model
3. Double exponential smoothing model
4. Moving average model (using 5 data points)

Option 1 : Simple exponential smoothing model

## Exponential Smoothing Method MCQ Question 12 Detailed Solution

Simple exponential smoothing model predicts the turning points quickly since it uses the concept of linear interpolation. This method can respond to any kind of noise signal immediately.

Brown’s quadratic smoothing model is suitable for linear trend series, it has smoothened forecast and it cannot predict turning points.

Double exponential smoothing model uses forecast and trend value. It is also known as Brown’s linear exponential smoothening. It is a smoothened value with seasonal adjustments.

# In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to

1. -1
2. zero
3. 0.5
4. 0.75
5. 1

Option 5 : 1

## Exponential Smoothing Method MCQ Question 13 Detailed Solution

Explanation:

In exponential smoothing method of forecast the forecast for the next period is equal to

Ft = α Dt-1 + (1 - α) Ft-1

If we further expand the expression

Ft = α Dt-1 + (1 - α) (α Dt-2 + (1-α) Ft-2

F= α Dt-1 + α (1-α ) Dt-2 + (1 - α )2 Ft-2

If we put the value of α = 0.8 (Close to 1) then,

Ft = 0.8 Dt-1 + 0.16 Dt-2 + 0.04 Ft-2

It can be observed from the above expression that recent data is given more weightage compared to the previous data, therefore, the higher value of exponential smoothing constant (Close to 1) is used for changing pattern of demand or to follow recent demand.

# Exponential smoothening methods are best suited under conditions when

1. forecasting horizon is relatively large
2. forecasting for large number of items
3. available outside information is more
4. All of the above

Option 1 : forecasting horizon is relatively large

## Exponential Smoothing Method MCQ Question 14 Detailed Solution

Concept:

Exponential smoothening methods are best suited under conditions when the forecasting horizon is relatively large so that exponential smoothing is very small and forecast error decreases.

# The sales data of a product for 5 years are Year 2014 2015 2016 2017 2018 Sales (units) 280 268 259 270 287 Assume the forecast for the year 2014 as 260 units. Using an exponential smoothing method with smoothing constant α = 0.5, the sales forecast (units) for the year 2019, is ______

## Exponential Smoothing Method MCQ Question 15 Detailed Solution

Concept:

Exponential Smoothing Method:

• In exponential smoothing method of forecast, the forecast for the next period is equal to
Ft = α Dt - 1 + (1 - α) Ft - 1 = Ft - 1 + α(Dt - 1 - Ft - 1)

Where, Dt-1 = latest figure sale or latest demand, Ft-1 = old forecast and α = smoothing constant

Calculation:

Given:

The sales of the particular years are given and the forecast for the year 2014, F2014 = 260 units.

∴ The forecast  for the year 2015,

F2015 = F2014 + α(D2014 - F2014

⇒ 260 + 0.5(280 - 260) = 270 units.

∴ The forecast  for the year 2016,

F2016 = F2015 + α(D2015 - F2015

⇒ 270 + 0.5(268 - 270) = 269 units.

∴ The forecast  for the year 2017,

F2017 = F2016 + α(D2016 - F2016

⇒ 269 + 0.5(259 - 269) = 264 units.

∴ The forecast  for the year 2018,

F2018 = F2017 + α(D2017 - F2017

⇒ 264 + 0.5(270 - 264) = 267 units.

∴ The forecast  for the year 2019,

F2019 = F2018 + α(D2018 - F2018

⇒ 267 + 0.5(287 - 267) = 277 units.

∴ The sales forecast for the year 2019, is 277 units.

# Using exponential smoothening, a car manufacturing company predicted the demand for that year as 1040 cars. The actual sale was found to be 1140 cars. If the company’s forecast for the next year is 1080, what is the value of the smoothening constant?

1. 0.4
2. 0.6
3. 0.7
4. 1.2

Option 1 : 0.4

## Exponential Smoothing Method MCQ Question 16 Detailed Solution

Concept:

Concept:

As per the exponential smoothening method:

Ft = Ft-1 + α[Dt-1 – Ft-1]

Where Dt - 1 is the demand for the previous period and Ft - 1 is the forecast of previous period and α is smoothing constant

Calculation:

Given:

Dt-1 = 1140, Ft-1 = 1040, Ft = 1080

Ft = Ft-1 + α[Dt-1 – Ft-1]

1080 = 1040 + α[1140 - 1040]

40 = α × 100

∴ α = 0.40

# The demand for a two-wheeler was 900 units and 1030 units in April 2015 and May 2015, respectively. The forecast for the month of April 2015 was 850 units. Considering a smoothing constant of 0.6, the forecast for the month of June 2015 is

1. 850 units
2. 927 units
3. 965 units
4. 970 units

Option 4 : 970 units

## Exponential Smoothing Method MCQ Question 17 Detailed Solution

Concept:

When smoothing constant is given use the following formula to calculate the forecast.

Ft = α Dt-1 + (1 - α) Ft-1

Calculation:

Given:

 Demand Forecasts April 900 850 May 1030 880 (calculated below) June

Calculation:

To find the forecast for the month of June using exponential smoothening.

We know that

Ft = α Dt-1 + (1 - α) Ft-1

Where ft is the forecast of current period, Ft-1 is the forecast of previous period, Dt-1 is the Demand for previous period.

So, for calculation of forecast for June, we need to calculate forecast of May.

FMay = α DA + (1 - α) FA

FMay = (0.6) (900) + (1 – 0.6) 850 = 880,

FJune = (0.6) DMay + (1 – 0.6) FMay

FJune = (0.6) (1030) + (0.4) (880)

∴ FJune = 970

# In a calendar year, the demand forecast of motorbikes for the month of June is 200. The actual demand of motorbikes for the month of June and July are 300 and 350, respectively. If single exponential smoothing method with smoothing constant 0.7 is used, then the demand forecast for the month of August is ______.

## Exponential Smoothing Method MCQ Question 18 Detailed Solution

Forecast for June (FJune) = 200

Demand for June (DJune) = 300

Demand for July (DJuly) = 350

Forecast for July (FJuly) = FJune + α (DJune - FJune)

FJuly = 200 + 0.7 (300 - 200) = 270

FAugust = FJuly + α (DJuly – FJuly)

= 270 + 0.7 (350 - 270) = 326

# The demand and forecast for February are 12000 and 10275, respectively. Using single exponential smoothening method (smoothening coefficient = 0.25), forecast for the month of March is

1. 431
2. 9587
3. 10706
4. 11000

Option 3 : 10706

## Exponential Smoothing Method MCQ Question 19 Detailed Solution

Concept:

𝐹𝑡+1 = 𝛼𝐷𝑡 + (1 − 𝛼) 𝐹𝑡 = 𝐹𝑡 + α (Dt - Ft)

This equation can be used when simple exponential smoothing is used as a forecasting model.

Here Ft represents the forecast for period t, Dt is the known demand for period t and α is the smoothing constant.

Calculation:

Given:

Forecast for February = 10275, Demand of February = 12000, smoothening coefficient = 0.25

Now,

Forecast for March:

FM = 10275 + 0.25 (12000 – 10275) = 10706.25

Hence option 3 will be the correct answer.
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