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A new exact algorithm for no-wait job shop problem to minimize makespan

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  • A. Ozolins

    (University of Latvia)

Abstract

In this paper, the no-wait job shop scheduling problem with a makespan objective is considered. A new exact algorithm, which is based on the dynamic programming (DP), is proposed. We introduce a dominance relation between two timetables. Several theorems are provided showing the application of the dominance. Despite the theoretical interest, experimental results prove that the proposed algorithm is able to optimally solve moderate benchmark instances within a reasonable time limit. Moreover, we have shown that the use of the dominance effectively reduces the state space of the algorithm. As an extension of the DP algorithm, we also present its heuristic version. It is shown that good quality upper bounds for large-size benchmark instances can be obtained. A comparison among several algorithms presented in the literature shows that the DP algorithm is quite competitive in terms of the computational time and the quality of obtained solutions.

Suggested Citation

  • A. Ozolins, 2020. "A new exact algorithm for no-wait job shop problem to minimize makespan," Operational Research, Springer, vol. 20(4), pages 2333-2363, December.
    • Handle: RePEc:spr:operea:v:20:y:2020:i:4:d:10.1007_s12351-018-0414-1
    DOI: 10.1007/s12351-018-0414-1
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    References listed on IDEAS

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    1. David Applegate & William Cook, 1991. "A Computational Study of the Job-Shop Scheduling Problem," INFORMS Journal on Computing, INFORMS, vol. 3(2), pages 149-156, May.
    2. Christoph Schuster, 2006. "No-wait Job Shop Scheduling: Tabu Search and Complexity of Subproblems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 473-491, July.
    3. J. Carlier & E. Pinson, 1989. "An Algorithm for Solving the Job-Shop Problem," Management Science, INFORMS, vol. 35(2), pages 164-176, February.
    4. Sartaj Sahni & Yookun Cho, 1979. "Complexity of Scheduling Shops with No Wait in Process," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 448-457, November.
    5. Robert H. Storer & S. David Wu & Renzo Vaccari, 1992. "New Search Spaces for Sequencing Problems with Application to Job Shop Scheduling," Management Science, INFORMS, vol. 38(10), pages 1495-1509, October.
    6. Mascis, Alessandro & Pacciarelli, Dario, 2002. "Job-shop scheduling with blocking and no-wait constraints," European Journal of Operational Research, Elsevier, vol. 143(3), pages 498-517, December.
    7. Zhu, Jie & Li, Xiaoping & Wang, Qian, 2009. "Complete local search with limited memory algorithm for no-wait job shops to minimize makespan," European Journal of Operational Research, Elsevier, vol. 198(2), pages 378-386, October.
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