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Scheduling Multiple Variable-Speed Machines

Author

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  • Michael A. Trick

    (Carnegie Mellon University, Pittsburgh, Pennsylvania)

Abstract

We examine scheduling problems where we control not only the assignment of jobs to machines, but also the time used by the job on the machine. For instance, many tooling machines allow control of the speed at which a job is run. Increasing the speed incurs costs due to machine wear, but also increases throughput. We discuss some fundamental scheduling problems in this environment and give algorithms for some interesting cases. Some cases are inherently difficult so for these we give heuristics. Our approach illustrates the exploitation of underlying network structure in combinatorial optimization problems. We create heuristics that optimally schedule a large portion of the jobs and then attempt to fit in the remainder. This also gives a method for quickly finding valid inequalities violated by the linear relaxation solution. For the problem of minimizing the sum of makespan and production costs, a rounding heuristic is within a constant factor of optimal. Our heuristics are compared to other classical heuristics.

Suggested Citation

  • Michael A. Trick, 1994. "Scheduling Multiple Variable-Speed Machines," Operations Research, INFORMS, vol. 42(2), pages 234-248, April.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:2:p:234-248
    DOI: 10.1287/opre.42.2.234
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    Cited by:

    1. Shabtay, Dvir, 2022. "Single-machine scheduling with machine unavailability periods and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 296(2), pages 423-439.
    2. Yaron Leyvand & Dvir Shabtay & George Steiner & Liron Yedidsion, 2010. "Just-in-time scheduling with controllable processing times on parallel machines," Journal of Combinatorial Optimization, Springer, vol. 19(3), pages 347-368, April.
    3. Dvir Shabtay & George Steiner, 2007. "Optimal Due Date Assignment and Resource Allocation to Minimize the Weighted Number of Tardy Jobs on a Single Machine," Manufacturing & Service Operations Management, INFORMS, vol. 9(3), pages 332-350, March.
    4. Jansen, Klaus & Mastrolilli, Monaldo & Solis-Oba, Roberto, 2005. "Approximation schemes for job shop scheduling problems with controllable processing times," European Journal of Operational Research, Elsevier, vol. 167(2), pages 297-319, December.
    5. Kayan, Rabia K. & Akturk, M. Selim, 2005. "A new bounding mechanism for the CNC machine scheduling problems with controllable processing times," European Journal of Operational Research, Elsevier, vol. 167(3), pages 624-643, December.
    6. Shabtay, Dvir & Zofi, Moshe, 2018. "Single machine scheduling with controllable processing times and an unavailability period to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 198(C), pages 191-200.
    7. Richard L. Daniels & Joseph B. Mazzola & Dailun Shi, 2004. "Flow Shop Scheduling with Partial Resource Flexibility," Management Science, INFORMS, vol. 50(5), pages 658-669, May.
    8. Sodhi, Manbir S. & Lamond, Bernard F. & Gautier, Antoine & Noel, Martin, 2001. "Heuristics for determining economic processing rates in a flexible manufacturing system," European Journal of Operational Research, Elsevier, vol. 129(1), pages 105-115, February.
    9. Bürgy, Reinhard & Bülbül, Kerem, 2018. "The job shop scheduling problem with convex costs," European Journal of Operational Research, Elsevier, vol. 268(1), pages 82-100.
    10. Gurel, Sinan & Akturk, M. Selim, 2007. "Optimal allocation and processing time decisions on non-identical parallel CNC machines: [epsilon]-constraint approach," European Journal of Operational Research, Elsevier, vol. 183(2), pages 591-607, December.
    11. 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.
    12. Dvir Shabtay & Moshe Kaspi, 2006. "Minimizing the makespan in open‐shop scheduling problems with a convex resource consumption function," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(3), pages 204-216, April.
    13. Lee, C. -Y. & Leon, V. J., 2001. "Machine scheduling with a rate-modifying activity," European Journal of Operational Research, Elsevier, vol. 128(1), pages 119-128, January.
    14. Shabtay, Dvir & Bensoussan, Yaron & Kaspi, Moshe, 2012. "A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flow-shop scheduling system," International Journal of Production Economics, Elsevier, vol. 136(1), pages 67-74.

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