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A simultaneous and iterative approach for parallel machine scheduling with sequence-dependent family setups

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Abstract

In this paper, we address a parallel machine scheduling problem to minimize the total weighted completion time, where product families are involved. Major setups occur when processing jobs of different families, and sequence dependencies are also taken into account. Considering its high practical relevance, we focus on the special case where all jobs of the same family have identical processing times. In order to avoid redundant setups, batching jobs of the same family can be performed. We first develop a variable neighborhood search algorithm (VNS) to solve the interrelated subproblems in a simultaneous manner. To further reduce computing time, we also propose an iterative scheme which alternates between a specific heuristic to form batches and a VNS scheme to schedule entire batches. Computational experiments are conducted which confirm the benefits of batching. Test results also show that both simultaneous and iterative approach outperform heuristics based on a fixed batch size and list scheduling. Furthermore, the iterative procedure succeeds in balancing solution quality and computing time.

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Acknowledgments

The authors would like to thank the anonymous referees for their constructive comments and valuable suggestions.

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Authors and Affiliations

  1. Department of Business and Economics, Technische Universitaet Dresden, 01069 , Dresden, Germany

    Liji Shen & Udo Buscher

  2. Department of Mathematics and Computer Science, University of Hagen, 58097 , Hagen, Germany

    Lars Mönch

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  1. Liji Shen
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  2. Lars Mönch
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  3. Udo Buscher
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Correspondence to Liji Shen.

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Shen, L., Mönch, L. & Buscher, U. A simultaneous and iterative approach for parallel machine scheduling with sequence-dependent family setups. J Sched 17, 471–487 (2014). https://doi.org/10.1007/s10951-013-0315-3

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  • DOI: https://doi.org/10.1007/s10951-013-0315-3

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