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A two-machine no-wait flow shop problem with two competing agents

Author

Listed:
  • Abdennour Azerine

    (Université des Sciences et de la Technologie Houari Boumedienne)

  • Mourad Boudhar

    (Université des Sciences et de la Technologie Houari Boumedienne)

  • Djamal Rebaine

    (Université du Québec à Chicoutimi)

Abstract

In this paper, we study the two-machine no-wait flow shop scheduling problem with two competing agents. The objective is to minimize the overall completion time of one agent subject to an upper bound on the makespan of the second agent. We proved the $$\mathcal {NP}$$ NP -hardness for three special cases: (1) each agent has exactly two operations. (2) the jobs of one agent require processing only on one machine, (3) the no-wait constraint is only required for the jobs of one agent. We exhibited polynomial time algorithms for other restricted cases. We also proposed a mathematical programming model and a branch and bound scheme as solving approaches for small-scale problems. For large instances, we present a tabu search meta-heuristic algorithm. An intensive experimental study is conducted to illustrate the effectiveness of the proposed exact and approximation algorithms.

Suggested Citation

  • Abdennour Azerine & Mourad Boudhar & Djamal Rebaine, 2022. "A two-machine no-wait flow shop problem with two competing agents," Journal of Combinatorial Optimization, Springer, vol. 43(1), pages 168-199, January.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:1:d:10.1007_s10878-021-00755-9
    DOI: 10.1007/s10878-021-00755-9
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    References listed on IDEAS

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    1. Sergey Kovalev & Mikhail Y. Kovalyov & Gur Mosheiov & Enrique Gerstl, 2019. "Semi-V-shape property for two-machine no-wait proportionate flow shop problem with TADC criterion," International Journal of Production Research, Taylor & Francis Journals, vol. 57(2), pages 560-566, January.
    2. Wenchang Luo & Lin Chen & Guochuan Zhang, 2012. "Approximation schemes for two-machine flow shop scheduling with two agents," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 229-239, October.
    3. Nicholas G. Hall & Chelliah Sriskandarajah, 1996. "A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process," Operations Research, INFORMS, vol. 44(3), pages 510-525, June.
    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. Allesandro Agnetis & Pitu B. Mirchandani & Dario Pacciarelli & Andrea Pacifici, 2004. "Scheduling Problems with Two Competing Agents," Operations Research, INFORMS, vol. 52(2), pages 229-242, April.
    6. Sriskandarajah, Chelliah & Ladet, Pierre, 1986. "Some no-wait shops scheduling problems: Complexity aspect," European Journal of Operational Research, Elsevier, vol. 24(3), pages 424-438, March.
    7. Allahverdi, Ali, 2016. "A survey of scheduling problems with no-wait in process," European Journal of Operational Research, Elsevier, vol. 255(3), pages 665-686.
    8. B Mor & G Mosheiov, 2014. "Polynomial time solutions for scheduling problems on a proportionate flowshop with two competing agents," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(1), pages 151-157, January.
    9. I. Adiri & D. Pohoryles, 1982. "Flowshop/no‐idle or no‐wait scheduling to minimize the sum of completion times," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(3), pages 495-504, September.
    10. Allahverdi, Ali & Aldowaisan, Tariq, 2004. "No-wait flowshops with bicriteria of makespan and maximum lateness," European Journal of Operational Research, Elsevier, vol. 152(1), pages 132-147, January.
    11. Mikhail A. Kubzin & Vitaly A. Strusevich, 2004. "Two‐machine flow shop no‐wait scheduling with a nonavailability interval," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 613-631, June.
    12. A Allahverdi & T Aldowaisan, 2002. "No-wait flowshops with bicriteria of makespan and total completion time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(9), pages 1004-1015, September.
    13. Peng Si Ow, 1985. "Focused Scheduling in Proportionate Flowshops," Management Science, INFORMS, vol. 31(7), pages 852-869, July.
    14. Alan S. Manne, 1960. "On the Job-Shop Scheduling Problem," Operations Research, INFORMS, vol. 8(2), pages 219-223, April.
    15. S. M. Johnson, 1954. "Optimal two‐ and three‐stage production schedules with setup times included," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 1(1), pages 61-68, March.
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