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A permutation flow-shop scheduling problem with convex models of operation processing times

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  • T.C.E. Cheng
  • A. Janiak

Abstract

The paper is an extension of the classical permutation flow-shop scheduling problem to the case where some of the job operation processing times are convex decreasing functions of the amounts of resources (e.g., financial outlay, energy, raw material) allocated to the operations (or machines on which they are performed). Some precedence constraints among the jobs are given. For this extended permutation flow-shop problem, the objective is to find a processing order of the jobs (which will be the same on each machine) and an allocation of a constrained resource so as to minimize the duration required to complete all jobs (i.e., the makespan). A computational complexity analysis of the problem shows that the problem is NP-hard. An analysis of the structure of the optimal solutions provides some elimination properties, which are exploited in a branch-and-bound solution scheme. Three approximate algorithms, together with the results of some computational experiments conducted to test the effectiveness of the algorithms, are also presented. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • T.C.E. Cheng & A. Janiak, 2000. "A permutation flow-shop scheduling problem with convex models of operation processing times," Annals of Operations Research, Springer, vol. 96(1), pages 39-60, November.
    • Handle: RePEc:spr:annopr:v:96:y:2000:i:1:p:39-60:10.1023/a:1018943300630
    DOI: 10.1023/A:1018943300630
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    Cited by:

    1. Shivam Gupta & Sachin Modgil & Samadrita Bhattacharyya & Indranil Bose, 2022. "Artificial intelligence for decision support systems in the field of operations research: review and future scope of research," Annals of Operations Research, Springer, vol. 308(1), pages 215-274, January.
    2. Lin-Hui Sun & Kai Cui & Ju-Hong Chen & Jun Wang & Xian-Chen He, 2013. "Some results of the worst-case analysis for flow shop scheduling with a learning effect," Annals of Operations Research, Springer, vol. 211(1), pages 481-490, December.
    3. Byung-Cheon Choi & Myoung-Ju Park, 2022. "Single-machine scheduling with resource-dependent processing times and multiple unavailability periods," Journal of Scheduling, Springer, vol. 25(2), pages 191-202, April.
    4. Wang, Sheng-yao & Wang, Ling & Liu, Min & Xu, Ye, 2013. "An effective estimation of distribution algorithm for solving the distributed permutation flow-shop scheduling problem," International Journal of Production Economics, Elsevier, vol. 145(1), pages 387-396.
    5. Shabtay, Dvir & Kaspi, Moshe, 2006. "Parallel machine scheduling with a convex resource consumption function," European Journal of Operational Research, Elsevier, vol. 173(1), pages 92-107, August.
    6. Leyvand, Yaron & Shabtay, Dvir & Steiner, George, 2010. "A unified approach for scheduling with convex resource consumption functions using positional penalties," European Journal of Operational Research, Elsevier, vol. 206(2), pages 301-312, October.

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