A Swift Heuristic Method for Work Order Scheduling under the
  Skilled-Workforce Constraint
  The considered problem is how to optimally allocate a set of jobs to
technicians of different skills such that the number of technicians of each
skill does not exceed the number of persons with that skill designation. The
key motivation is the quick sensitivity analysis in terms of the workforce size
which is quite necessary in many industries in the presence of unexpected work
orders. A time-indexed mathematical model is proposed to minimize the total
weighted completion time of the jobs. The proposed model is decomposed into a
number of single-skill sub-problems so that each one is a combination of a
series of nested binary Knapsack problems. A heuristic procedure is proposed to
solve the problem. Our experimental results, based on a real-world case study,
reveal that the proposed method quickly produces a schedule statistically close
to the optimal one while the classical optimal procedure is very
time-consuming.
