A mixed-integer goal-programming formulation of the standard flow-shop scheduling problem

Willem J. Selen

Research output: Contribution to journalArticlepeer-review

69 Citations (Scopus)


Until recently, the majority of models used to find an optimal sequence for the standard flow-shop problem were based on a single objective, typically makespan. In many applications, the practitioner may also want to consider other criteria simultaneously, such as mean flow-time or throughput time. As makespan and flow-time are equivalent criteria for optimizing machine idle-time and job idle-time, respectively, these additional criteria could be inherently considered as well. The effect of job idle-time, measuring in-process inventory, could be of particular importance. This paper presents an extension of an earlier model developed by the authors, formulating the generalized A job, M machine standard flow-shop problem as a mixed-integer goal-programming model. The formulation was empirically tested through a comparison of the generated optimal solutions to their mathematically derived counterparts. For this, a special flow-shop problem with certain permutation properties was selected. In addition, a randomly chosen problem was solved to show the general applicability of the derived formulation. The model allows the incorporation of the makespan as well as the mean flow-time criteria, instead of optimization being based on a single objective.

Original languageEnglish
Pages (from-to)1121-1128
Number of pages8
JournalJournal of the Operational Research Society
Issue number12
Publication statusPublished - Dec 1986
Externally publishedYes


  • Goal programming
  • Multiple objectives
  • Production
  • Scheduling

ASJC Scopus subject areas

  • Modelling and Simulation
  • Strategy and Management
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research


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