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Minimizing Makespan in a Class of Reentrant Shops

Author

Listed:
  • M. Y. Wang

    (University of Toronto, Toronto, Canada)

  • S. P. Sethi

    (University of Texas, Dallas)

  • S. L. van de Velde

    (Erasmus University, Rotterdam, The Netherlands)

Abstract

We study the problem of scheduling a chain-reentrant shop, in which each job goes for its processing first to a machine called the primary machine, then to a number of other machines in a fixed sequence, and finally back to the primary machine for its last operation. The problem is to schedule the jobs so as to minimize the makespan. This problem is unary NP -hard for a general number of machines. We focus in particular on the two-machine case that is also at least binary NP -hard. We prove some properties that identify a specific class of optimal schedules, and then use these properties in designing an approximation algorithm and a branch-and-bound type optimization algorithm. The approximation algorithm, of which we present three versions, has a worst-case performance guarantee of 3/2 along with an excellent empirical performance. The optimization algorithm solves large instances quickly. Finally, we identify a few well solvable special cases and present a pseudo-polynomial algorithm for the case in which the first and the last operations of any job (on the primary machine) are identical.

Suggested Citation

  • M. Y. Wang & S. P. Sethi & S. L. van de Velde, 1997. "Minimizing Makespan in a Class of Reentrant Shops," Operations Research, INFORMS, vol. 45(5), pages 702-712, October.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:5:p:702-712
    DOI: 10.1287/opre.45.5.702
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    Citations

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    Cited by:

    1. S-W Choi & Y-D Kim, 2007. "Minimizing makespan on a two-machine re-entrant flowshop," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(7), pages 972-981, July.
    2. Allahverdi, Ali & Aldowaisan, Tariq, 2002. "New heuristics to minimize total completion time in m-machine flowshops," International Journal of Production Economics, Elsevier, vol. 77(1), pages 71-83, May.
    3. Choi, Seong-Woo & Kim, Yeong-Dae, 2009. "Minimizing total tardiness on a two-machine re-entrant flowshop," European Journal of Operational Research, Elsevier, vol. 199(2), pages 375-384, December.
    4. 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.
    5. S. M. Mousavi & I. Mahdavi & J. Rezaeian & M. Zandieh, 2018. "An efficient bi-objective algorithm to solve re-entrant hybrid flow shop scheduling with learning effect and setup times," Operational Research, Springer, vol. 18(1), pages 123-158, April.
    6. Aldowaisan, Tariq & Allahverdi, Ali, 2004. "New heuristics for m-machine no-wait flowshop to minimize total completion time," Omega, Elsevier, vol. 32(5), pages 345-352, October.
    7. JC-H Pan & J-S Chen, 2003. "Minimizing makespan in re-entrant permutation flow-shops," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(6), pages 642-653, June.
    8. Baptiste, Pierre, 2006. "Stochastic algorithms: Using the worst to reach the best," International Journal of Production Economics, Elsevier, vol. 99(1-2), pages 41-51, February.
    9. Yu, Tae-Sun & Pinedo, Michael, 2020. "Flow shops with reentry: Reversibility properties and makespan optimal schedules," European Journal of Operational Research, Elsevier, vol. 282(2), pages 478-490.
    10. Wang, Kai & Qin, Hu & Huang, Yun & Luo, Mengwen & Zhou, Lei, 2021. "Surgery scheduling in outpatient procedure centre with re-entrant patient flow and fuzzy service times," Omega, Elsevier, vol. 102(C).
    11. Al-Anzi, Fawaz S. & Allahverdi, Ali, 2007. "A self-adaptive differential evolution heuristic for two-stage assembly scheduling problem to minimize maximum lateness with setup times," European Journal of Operational Research, Elsevier, vol. 182(1), pages 80-94, October.
    12. A Allahverdi & F S Al-Anzi, 2006. "Scheduling multi-stage parallel-processor services to minimize average response time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(1), pages 101-110, January.
    13. Yang, Dar-Li & Kuo, Wen-Hung & Chern, Maw-Sheng, 2008. "Multi-family scheduling in a two-machine reentrant flow shop with setups," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1160-1170, June.
    14. Karim Amrouche & Mourad Boudhar & Mohamed Bendraouche & Farouk Yalaoui, 2017. "Chain-reentrant shop with an exact time lag: new results," International Journal of Production Research, Taylor & Francis Journals, vol. 55(1), pages 285-295, January.

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