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Dual criteria preemptive open‐shop problems with minimum makespan

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  • George Vairaktarakis
  • Sartaj Sahni

Abstract

In this article we present an algorithm for the minimum makespan preemptive open shop, which is superior to existing algorithms in both space and time requirements. We define the more complex generalized open shop and flexible open shop and address the minimum makespan problem on these shops. We show how we can use the algorithm for the minimum makespan open shop to achieve load balancing in simple and generalized open shops without increasing the complexity of the algorithm. Load balancing dictates that the number of busy machines in each period is as even as possible. We also consider preventive maintenance issues in the open shop, and makespan retains its minimum value. In particular we consider the scenario where a machine can be maintained during any period that it happens to be idle. Also we consider the case that a maintenance schedule is prespecified. We show that this problem can be solved via a linear programming formulation that can also take into account release times for the jobs and ready times for the machines. Faster algorithms are presented for open shops with three machines or less. © 1995 John Wiley & Sons, Inc.

Suggested Citation

  • George Vairaktarakis & Sartaj Sahni, 1995. "Dual criteria preemptive open‐shop problems with minimum makespan," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(1), pages 103-121, February.
    • Handle: RePEc:wly:navres:v:42:y:1995:i:1:p:103-121
    DOI: 10.1002/1520-6750(199502)42:13.0.CO;2-R
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    References listed on IDEAS

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    1. E. L. Lawler & J. K. Lenstra & A. H. G. Rinnooy Kan, 1981. "Minimizing Maximum Lateness in a Two-Machine Open Shop," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 153-158, February.
    2. Teofilo Gonzalez, 1982. "Unit Execution Time Shop Problems," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 57-66, February.
    3. Yookun Cho & Sartaj Sahni, 1981. "Preemptive Scheduling of Independent Jobs with Release and Due Times on Open, Flow and Job Shops," Operations Research, INFORMS, vol. 29(3), pages 511-522, June.
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    1. Ahmadian, Mohammad Mahdi & Khatami, Mostafa & Salehipour, Amir & Cheng, T.C.E., 2021. "Four decades of research on the open-shop scheduling problem to minimize the makespan," European Journal of Operational Research, Elsevier, vol. 295(2), pages 399-426.
    2. M.A. Kubzin & V.A. Strusevich & J. Breit & G. Schmidt, 2006. "Polynomial‐time approximation schemes for two‐machine open shop scheduling with nonavailability constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(1), pages 16-23, February.

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