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Scheduling with cardinality dependent unavailability periods

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  • Jaykrishnan, G.
  • Levin, Asaf

Abstract

We consider non-preemptive scheduling problems on parallel identical machines where machines change their status from being available to being unavailable and vice versa along the time horizon. The particular form of unavailability we consider is when the starting time of each downtime depends upon the cardinality of the job subset processed on that machine since the previous downtime. We consider the problem of minimizing the makespan in such scenarios as well as its dual problem where we have a fixed common deadline of 1 and the goal is to minimize the number of machines for which there is a feasible schedule. We develop an EPTAS for the first variant and an AFPTAS for the second variant.

Suggested Citation

  • Jaykrishnan, G. & Levin, Asaf, 2024. "Scheduling with cardinality dependent unavailability periods," European Journal of Operational Research, Elsevier, vol. 316(2), pages 443-458.
    • Handle: RePEc:eee:ejores:v:316:y:2024:i:2:p:443-458
    DOI: 10.1016/j.ejor.2024.02.038
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    References listed on IDEAS

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    1. Liu, Zhixin & Lu, Liang & Qi, Xiangtong, 2018. "Cost allocation in rescheduling with machine unavailable period," European Journal of Operational Research, Elsevier, vol. 266(1), pages 16-28.
    2. Schmidt, Gunter, 2000. "Scheduling with limited machine availability," European Journal of Operational Research, Elsevier, vol. 121(1), pages 1-15, February.
    3. M Ozlen & M Azizoğlu, 2011. "Rescheduling unrelated parallel machines with total flow time and total disruption cost criteria," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 152-164, January.
    4. Ping Ji & Lin Li, 2015. "Single-Machine Group Scheduling Problems with Variable Job Processing Times," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, July.
    5. Guoqing Wang & Hongyi Sun & Chengbin Chu, 2005. "Preemptive Scheduling with Availability Constraints to Minimize Total Weighted Completion Times," Annals of Operations Research, Springer, vol. 133(1), pages 183-192, January.
    6. H. Kellerer & U. Pferschy, 1999. "Cardinality constrained bin‐packing problems," Annals of Operations Research, Springer, vol. 92(0), pages 335-348, January.
    7. H. W. Lenstra, 1983. "Integer Programming with a Fixed Number of Variables," Mathematics of Operations Research, INFORMS, vol. 8(4), pages 538-548, November.
    8. Alberto Caprara & Hans Kellerer & Ulrich Pferschy, 2003. "Approximation schemes for ordered vector packing problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(1), pages 58-69, February.
    9. Vitaly A. Strusevich & Kabir Rustogi, 2017. "Scheduling with Flexible Maintenance," International Series in Operations Research & Management Science, in: Scheduling with Time-Changing Effects and Rate-Modifying Activities, chapter 0, pages 291-315, Springer.
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