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Mean Flow Time Minimization in Reentrant Job Shops with a Hub

Author

Listed:
  • Wieslaw Kubiak

    (Memorial University of Newfoundland, St. John's, Newfoundland, Canada)

  • Sheldon X. C. Lou

    (California State University San Marcos, San Marcos, California)

  • Yingmeng Wang

    (University of Toronto, Toronto, Ontario, Canada)

Abstract

This paper considers a reentrant job shop with one hub machine which a job enters K times. Between any two consecutive entries into the hub, the job is processed on other machines. The objective is to minimize the total flow time. Under two key assumptions, the bottleneck assumption and the hereditary order (HO) assumption on the processing times of the entries, it is proved that there is an optimal schedule with the shortest processing time (SPT) job order and a dynamic programming algorithm is derived to find such a schedule. An approximation algorithm based on the shortest path algorithm and the SPT job order is also proposed to solve the problem. The approximation algorithm finds an optimal clustered schedule. In clustered schedules, jobs are scheduled in disjoint clusters; they resemble batch processing and seem to be of practical importance. Worst-case bounds for clustered schedules are proved with the HO assumption relaxed. Two special cases with the restriction that there are only two entries to the hub machine are further analyzed to offer more insight into the structure of optimal solutions.

Suggested Citation

  • Wieslaw Kubiak & Sheldon X. C. Lou & Yingmeng Wang, 1996. "Mean Flow Time Minimization in Reentrant Job Shops with a Hub," Operations Research, INFORMS, vol. 44(5), pages 764-776, October.
    • Handle: RePEc:inm:oropre:v:44:y:1996:i:5:p:764-776
    DOI: 10.1287/opre.44.5.764
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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. 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.
    3. 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.
    4. 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.
    5. Wieslaw Kubiak & Yanling Feng & Guo Li & Suresh P. Sethi & Chelliah Sriskandarajah, 2020. "Efficient algorithms for flexible job shop scheduling with parallel machines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(4), pages 272-288, June.
    6. Ali Obeid & Stéphane Dauzère-Pérès & Claude Yugma, 2014. "Scheduling job families on non-identical parallel machines with time constraints," Annals of Operations Research, Springer, vol. 213(1), pages 221-234, February.

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