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Scheduling interfering job sets on parallel machines

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  • Balasubramanian, Hari
  • Fowler, John
  • Keha, Ahmet
  • Pfund, Michele

Abstract

We consider bicriteria scheduling on identical parallel machines in a nontraditional context: jobs belong to two disjoint sets, and each set has a different criterion to be minimized. The jobs are all available at time zero and have to be scheduled (non-preemptively) on m parallel machines. The goal is to generate the set of all non-dominated solutions, so the decision maker can evaluate the tradeoffs and choose the schedule to be implemented. We consider the case where, for one of the two sets, the criterion to be minimized is makespan while for the other the total completion time needs to be minimized. Given that the problem is NP-hard, we propose an iterative SPT-LPT-SPT heuristic and a bicriteria genetic algorithm for the problem. Both approaches are designed to exploit the problem structure and generate a set of non-dominated solutions. In the genetic algorithm we use a special encoding scheme and also a unique strategy - based on the properties of a non-dominated solution - to ensure that all parts of the non-dominated front are explored. The heuristic and the genetic algorithm are compared with a time-indexed integer programming formulation for small and large instances. Results indicate that the both the heuristic and the genetic algorithm provide high solution quality and are computationally efficient. The heuristics proposed also have the potential to be generalized for the problem of interfering job sets involving other bicriteria pairs.

Suggested Citation

  • Balasubramanian, Hari & Fowler, John & Keha, Ahmet & Pfund, Michele, 2009. "Scheduling interfering job sets on parallel machines," European Journal of Operational Research, Elsevier, vol. 199(1), pages 55-67, November.
    • Handle: RePEc:eee:ejores:v:199:y:2009:i:1:p:55-67
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    References listed on IDEAS

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    5. SOUSA, Jorge P. & WOLSEY, Laurence A., 1992. "A time indexed formulation of non-preemptive single machine scheduling problems," LIDAM Reprints CORE 984, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Citations

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    Cited by:

    1. Perez-Gonzalez, Paz & Framinan, Jose M., 2014. "A common framework and taxonomy for multicriteria scheduling problems with interfering and competing jobs: Multi-agent scheduling problems," European Journal of Operational Research, Elsevier, vol. 235(1), pages 1-16.
    2. Cheng, Shuenn-Ren, 2014. "Some new problems on two-agent scheduling to minimize the earliness costs," International Journal of Production Economics, Elsevier, vol. 156(C), pages 24-30.
    3. Kejun Zhao & Xiwen Lu, 2016. "Two approximation algorithms for two-agent scheduling on parallel machines to minimize makespan," Journal of Combinatorial Optimization, Springer, vol. 31(1), pages 260-278, January.
    4. Paz Perez-Gonzalez & Jose M. Framinan, 2018. "Single machine interfering jobs problem with flowtime objective," Journal of Intelligent Manufacturing, Springer, vol. 29(5), pages 953-972, June.
    5. Donatas Elvikis & Vincent T’kindt, 2014. "Two-agent scheduling on uniform parallel machines with min-max criteria," Annals of Operations Research, Springer, vol. 213(1), pages 79-94, February.
    6. Yang-Kuei Lin & Tzu-Yueh Yin, 2022. "Generating bicriteria schedules for correlated parallel machines involving tardy jobs and weighted completion time," Annals of Operations Research, Springer, vol. 319(2), pages 1655-1688, December.
    7. Lang, Fabian & Fink, Andreas & Brandt, Tobias, 2016. "Design of automated negotiation mechanisms for decentralized heterogeneous machine scheduling," European Journal of Operational Research, Elsevier, vol. 248(1), pages 192-203.
    8. Choi, Byung-Cheon & Park, Myoung-Ju, 2017. "Two-agent parallel machine scheduling with a restricted number of overlapped reserved tasks," European Journal of Operational Research, Elsevier, vol. 260(2), pages 514-519.

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