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Two-machine flow shop scheduling to minimize the sum of maximum earliness and tardiness

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  • Moslehi, G.
  • Mirzaee, M.
  • Vasei, M.
  • Modarres, M.
  • Azaron, A.

Abstract

This paper presents optimal scheduling in a two-machine flow shop, in which the objective function is to minimize the sum of maximum earliness and tardiness (n/2/P/ETmax). Since this problem tries to minimize earliness and tardiness, the results can be useful for different production systems such as just in time (JIT). This objective function has already been considered for n jobs and m machines, but the proposed algorithms are not efficient to solve large scale problems. In this paper, neighborhood conditions are developed and the dominant set for any optimal solution is determined. The branch-and-bound (B&B) method is used to solve the problem and the proper upper and lower bounds are also introduced. A number of effective lemmas are introduced to develop an algorithm which is more efficient than those already known. To show the effectiveness of the proposed algorithm, 380 problems of different sizes are randomly generated and solved. More than 82% of the problems are shown to reach optimal solutions.

Suggested Citation

  • Moslehi, G. & Mirzaee, M. & Vasei, M. & Modarres, M. & Azaron, A., 2009. "Two-machine flow shop scheduling to minimize the sum of maximum earliness and tardiness," International Journal of Production Economics, Elsevier, vol. 122(2), pages 763-773, December.
    • Handle: RePEc:eee:proeco:v:122:y:2009:i:2:p:763-773
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    References listed on IDEAS

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    1. Sung, C. S. & Min, J. I., 2001. "Scheduling in a two-machine flowshop with batch processing machine(s) for earliness/tardiness measure under a common due date," European Journal of Operational Research, Elsevier, vol. 131(1), pages 95-106, May.
    2. Koulamas, Christos, 1998. "On the complexity of two-machine flowshop problems with due date related objectives," European Journal of Operational Research, Elsevier, vol. 106(1), pages 95-100, April.
    3. Peng Si Ow & Thomas E. Morton, 1989. "The Single Machine Early/Tardy Problem," Management Science, INFORMS, vol. 35(2), pages 177-191, February.
    4. Nawaz, Muhammad & Enscore Jr, E Emory & Ham, Inyong, 1983. "A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem," Omega, Elsevier, vol. 11(1), pages 91-95.
    5. Lin, Bertrand M. T., 2001. "Scheduling in the two-machine flowshop with due date constraints," International Journal of Production Economics, Elsevier, vol. 70(2), pages 117-123, March.
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    Citations

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    Cited by:

    1. Li, Shisheng & Ng, C.T. & Yuan, Jinjiang, 2011. "Group scheduling and due date assignment on a single machine," International Journal of Production Economics, Elsevier, vol. 130(2), pages 230-235, April.
    2. Imen Hamdi & Imen Boujneh, 2022. "Particle swarm optimization based-algorithms to solve the two-machine cross-docking flow shop problem: just in time scheduling," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 947-969, September.
    3. Mehravaran, Yasaman & Logendran, Rasaratnam, 2012. "Non-permutation flowshop scheduling in a supply chain with sequence-dependent setup times," International Journal of Production Economics, Elsevier, vol. 135(2), pages 953-963.
    4. Yenisey, Mehmet Mutlu & Yagmahan, Betul, 2014. "Multi-objective permutation flow shop scheduling problem: Literature review, classification and current trends," Omega, Elsevier, vol. 45(C), pages 119-135.
    5. Schaller, Jeffrey & Valente, Jorge M.S., 2020. "Minimizing total earliness and tardiness in a nowait flow shop," International Journal of Production Economics, Elsevier, vol. 224(C).
    6. Pang, King-Wah, 2013. "A genetic algorithm based heuristic for two machine no-wait flowshop scheduling problems with class setup times that minimizes maximum lateness," International Journal of Production Economics, Elsevier, vol. 141(1), pages 127-136.
    7. Vahid Nasrollahi & Ghasem Moslehi & Mohammad Reisi-Nafchi, 2022. "Minimizing the weighted sum of maximum earliness and maximum tardiness in a single-agent and two-agent form of a two-machine flow shop scheduling problem," Operational Research, Springer, vol. 22(2), pages 1403-1442, April.

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