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Single machine scheduling with controllable processing times and an unavailability period to minimize the makespan

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  • Shabtay, Dvir
  • Zofi, Moshe

Abstract

We study a single machine scheduling problem, where job processing times are controllable, and there is a fixed machine unavailability interval. We assume that the job processing time is a convex decreasing function of the amount of resource allocated to its processing operation. We further assume that there is a budget restriction on the total resource allocation cost. Our aim is to find a job schedule that minimizes the makespan. We prove that the problem is NP-hard and develop both a constant factor approximation algorithm and a fully polynomial time approximation scheme (FPTAS) for solving it. The FPTAS is obtained despite the fact that we could not design a pseudo-polynomial time algorithm for finding the optimal solution.

Suggested Citation

  • Shabtay, Dvir & Zofi, Moshe, 2018. "Single machine scheduling with controllable processing times and an unavailability period to minimize the makespan," International Journal of Production Economics, Elsevier, vol. 198(C), pages 191-200.
    • Handle: RePEc:eee:proeco:v:198:y:2018:i:c:p:191-200
    DOI: 10.1016/j.ijpe.2017.12.025
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    References listed on IDEAS

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    1. Oron, Daniel, 2016. "Scheduling controllable processing time jobs with position-dependent workloads," International Journal of Production Economics, Elsevier, vol. 173(C), pages 153-160.
    2. Chung-Yee Lee & Lei Lei, 2001. "Multiple-Project Scheduling with Controllable Project Duration and Hard Resource Constraint: Some Solvable Cases," Annals of Operations Research, Springer, vol. 102(1), pages 287-307, February.
    3. Yang, Dar-Li & Lai, Chien-Jung & Yang, Suh-Jenq, 2014. "Scheduling problems with multiple due windows assignment and controllable processing times on a single machine," International Journal of Production Economics, Elsevier, vol. 150(C), pages 96-103.
    4. Liao, Ching-Jong & Shyur, Der-Lin & Lin, Chien-Hung, 2005. "Makespan minimization for two parallel machines with an availability constraint," European Journal of Operational Research, Elsevier, vol. 160(2), pages 445-456, January.
    5. Schmidt, Gunter, 2000. "Scheduling with limited machine availability," European Journal of Operational Research, Elsevier, vol. 121(1), pages 1-15, February.
    6. Clyde L. Monma & Alexander Schrijver & Michael J. Todd & Victor K. Wei, 1990. "Convex Resource Allocation Problems on Directed Acyclic Graphs: Duality, Complexity, Special Cases, and Extensions," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 736-748, November.
    7. Leyvand, Yaron & Shabtay, Dvir & Steiner, George, 2010. "A unified approach for scheduling with convex resource consumption functions using positional penalties," European Journal of Operational Research, Elsevier, vol. 206(2), pages 301-312, October.
    8. Yaron Leyvand & Dvir Shabtay & George Steiner, 2010. "Optimal delivery time quotation to minimize total tardiness penalties with controllable processing times," IISE Transactions, Taylor & Francis Journals, vol. 42(3), pages 221-231.
    9. Daniel Oron, 2016. "Scheduling controllable processing time jobs in a deteriorating environment," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(3), pages 535-535, March.
    10. Imed Kacem, 2009. "Approximation algorithms for the makespan minimization with positive tails on a single machine with a fixed non-availability interval," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 117-133, February.
    11. Liu, Peihai & Lu, Xiwen, 2016. "Integrated production and job delivery scheduling with an availability constraint," International Journal of Production Economics, Elsevier, vol. 176(C), pages 1-6.
    12. Kayan, Rabia K. & Akturk, M. Selim, 2005. "A new bounding mechanism for the CNC machine scheduling problems with controllable processing times," European Journal of Operational Research, Elsevier, vol. 167(3), pages 624-643, December.
    13. Allaoui, H. & Artiba, A. & Elmaghraby, S.E. & Riane, F., 2006. "Scheduling of a two-machine flowshop with availability constraints on the first machine," International Journal of Production Economics, Elsevier, vol. 99(1-2), pages 16-27, February.
    14. J. Breit & G. Schmidt & V. A. Strusevich, 2003. "Non-preemptive two-machine open shop scheduling with non-availability constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(2), pages 217-234, May.
    15. Kacem, Imed & Chu, Chengbin, 2008. "Worst-case analysis of the WSPT and MWSPT rules for single machine scheduling with one planned setup period," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1080-1089, June.
    16. Shabtay, Dvir & Kaspi, Moshe, 2002. "Optimization of the machining economics problem under the failure replacement strategy," International Journal of Production Economics, Elsevier, vol. 80(3), pages 213-230, December.
    17. Kacem, Imed & Chu, Chengbin, 2008. "Efficient branch-and-bound algorithm for minimizing the weighted sum of completion times on a single machine with one availability constraint," International Journal of Production Economics, Elsevier, vol. 112(1), pages 138-150, March.
    18. Breit, Joachim, 2007. "Improved approximation for non-preemptive single machine flow-time scheduling with an availability constraint," European Journal of Operational Research, Elsevier, vol. 183(2), pages 516-524, December.
    19. Dvir Shabtay & George Steiner, 2008. "The single-machine earliness-tardiness scheduling problem with due date assignment and resource-dependent processing times," Annals of Operations Research, Springer, vol. 159(1), pages 25-40, March.
    20. Michael A. Trick, 1994. "Scheduling Multiple Variable-Speed Machines," Operations Research, INFORMS, vol. 42(2), pages 234-248, April.
    21. Janiak, Adam & Kovalyov, Mikhail Y., 1996. "Single machine scheduling subject to deadlines and resource dependent processing times," European Journal of Operational Research, Elsevier, vol. 94(2), pages 284-291, October.
    22. Shabtay, Dvir & Bensoussan, Yaron & Kaspi, Moshe, 2012. "A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flow-shop scheduling system," International Journal of Production Economics, Elsevier, vol. 136(1), pages 67-74.
    23. Sadfi, Cherif & Penz, Bernard & Rapine, Christophe & Blazewicz, Jacek & Formanowicz, Piotr, 2005. "An improved approximation algorithm for the single machine total completion time scheduling problem with availability constraints," European Journal of Operational Research, Elsevier, vol. 161(1), pages 3-10, February.
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    7. Ali Kordmostafapour & Javad Rezaeian & Iraj Mahdavi & Mahdi Yar Farjad, 2022. "Scheduling unrelated parallel machine problem with multi-mode processing times and batch delivery cost," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1438-1470, December.

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