Optimal job-shop scheduling with random operations and cost objectives

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43 Scopus citations


We consider a job-shop manufacturing cell of n jobs (orders), Ji, 1≤i≤n, and m machines Mk, 1≤k≤m. Each job-operation Oiℓ (the ℓth operation of job i) has a random time duration tiℓ with the average value t̄iℓ and the variance Viℓ. Each job Ji has its due date Di and the penalty cost C*i for not delivering the job on time (to be paid once to the customer). An additional penalty C**i has to be paid for each time unit of delay, i.e., when waiting for the job's delivery after the due date. If job Ji is accomplished before Di it has to be stored until the due date with the expenses C***i per time unit. The problem is to determine optimal earliest start times Si of jobs Ji, 1≤i≤n, in order to minimize the average value of total penalty and storage expenses. Three basic principles are incorporated in the model: (1) At each time moment when several jobs are ready to be served on one and the same machine, a competition among them is introduced. It is based on the newly developed heuristic decision-making rule with cost objectives. (2) A simulation model of manufacturing the job-shop and comprising decision-making for each competitive situation, is developed. (3) Optimization is carried out by applying to the simulation model the coordinate descent search method. The variables to be optimized are the earliest start times Si. A numerical example of a simulation run is presented to clarify the decision-making rule. The optimization model is verified via extensive simulation.

Original languageEnglish
Pages (from-to)147-157
Number of pages11
JournalInternational Journal of Production Economics
Issue number2
StatePublished - 21 Mar 2002


  • Coordinate descent search algorithm
  • Job-shop problem
  • Pairwise comparison
  • Random operation
  • Total penalty and storage expenses

ASJC Scopus subject areas

  • General Business, Management and Accounting
  • Economics and Econometrics
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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