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Scheduling with machine cost and rejection

Author

Listed:
  • György Dósa

    (Pannon University)

  • Yong He

    (Zhejiang University)

Abstract

In this paper we consider the scheduling problem with machine cost and rejection penalties. For this problem, we are given a sequence of independent jobs, each being characterized by its processing time (size) and its penalty. No machine is initially provided, and when a job is revealed the algorithm has the option to purchase new machines. Right when a new job arrives, we have the following choices: (i) reject it, in which case we pay its penalty; (ii) non-preemptively process it on an existing machine, which contributes to the machine load; (iii) purchase a new machine, and assign it to this machine. The objective is to minimize the sum of the makespan, the cost for purchasing machines, and the total penalty of all rejected jobs. For the small job case, (where all jobs have sizes no greater than the cost for purchasing one machine, and which is the generalization of the Ski-Rental Problem) we present an optimal online algorithm with a competitive ratio of 2.

Suggested Citation

  • György Dósa & Yong He, 2006. "Scheduling with machine cost and rejection," Journal of Combinatorial Optimization, Springer, vol. 12(4), pages 337-350, December.
    • Handle: RePEc:spr:jcomop:v:12:y:2006:i:4:d:10.1007_s10878-006-9003-y
    DOI: 10.1007/s10878-006-9003-y
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    Citations

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    Cited by:

    1. Ivo Blöchliger & Nicolas Zufferey, 2013. "Multi-coloring and job-scheduling with assignment and incompatibility costs," Annals of Operations Research, Springer, vol. 211(1), pages 83-101, December.
    2. Liqi Zhang & Lingfa Lu & Shisheng Li, 2016. "New results on two-machine flow-shop scheduling with rejection," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1493-1504, May.
    3. Yinfeng Xu & Rongteng Zhi & Feifeng Zheng & Ming Liu, 2022. "Competitive algorithm for scheduling of sharing machines with rental discount," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 414-434, August.
    4. Islam Akaria & Leah Epstein, 2020. "An optimal online algorithm for scheduling with general machine cost functions," Journal of Scheduling, Springer, vol. 23(2), pages 155-162, April.
    5. Ma, Ran & Yuan, Jinjiang, 2014. "Online tradeoff scheduling on a single machine to minimize makespan and total weighted completion time," International Journal of Production Economics, Elsevier, vol. 158(C), pages 114-119.
    6. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, July.
    7. Lu, Lingfa & Ng, C.T. & Zhang, Liqi, 2011. "Optimal algorithms for single-machine scheduling with rejection to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 130(2), pages 153-158, April.
    8. Zhang, Liqi & Lu, Lingfa & Yuan, Jinjiang, 2009. "Single machine scheduling with release dates and rejection," European Journal of Operational Research, Elsevier, vol. 198(3), pages 975-978, November.
    9. A J Ruiz-Torres & F J López & P J Wojciechowski & J C Ho, 2010. "Parallel machine scheduling problems considering regular measures of performance and machine cost," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 849-857, May.
    10. Liqi Zhang & Lingfa Lu, 2016. "Parallel-machine scheduling with release dates and rejection," 4OR, Springer, vol. 14(2), pages 165-172, June.

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