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An efficient bicriteria algorithm for stable robotic flow shop scheduling

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  • Che, Ada
  • Kats, Vladimir
  • Levner, Eugene

Abstract

We consider a flow shop for processing single type of parts serviced by a single robot. The robot transportation times are allowed to have small perturbations. We treat the robotic flow shop scheduling problem considering stability of its schedule where the robot route is fixed and the processing durations of parts are to be specified from given intervals. The stability radius of a schedule is defined as the largest quantity of variations in the transportation times within which the schedule can still be executed as expected. We consider the bicriteria optimization problem which consists of minimizing the cycle time and maximizing the stability radius. The objective is to handle the two criteria simultaneously, that is, to find their Pareto front. We propose a new strongly polynomial algorithm for finding the minimum cycle times for all possible values of stability radius with time complexity of O(m4), where m is the number of processing machines in the flow shop. This implies that we can find the entire Pareto front of the problem in O(m4) time.

Suggested Citation

  • Che, Ada & Kats, Vladimir & Levner, Eugene, 2017. "An efficient bicriteria algorithm for stable robotic flow shop scheduling," European Journal of Operational Research, Elsevier, vol. 260(3), pages 964-971.
    • Handle: RePEc:eee:ejores:v:260:y:2017:i:3:p:964-971
    DOI: 10.1016/j.ejor.2017.01.033
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    References listed on IDEAS

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    1. Che, Ada & Feng, Jianguang & Chen, Haoxun & Chu, Chengbin, 2015. "Robust optimization for the cyclic hoist scheduling problem," European Journal of Operational Research, Elsevier, vol. 240(3), pages 627-636.
    2. 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.
    3. Kats, Vladimir & Levner, Eugene, 2011. "A faster algorithm for 2-cyclic robotic scheduling with a fixed robot route and interval processing times," European Journal of Operational Research, Elsevier, vol. 209(1), pages 51-56, February.
    4. Herroelen, Willy & Leus, Roel, 2005. "Project scheduling under uncertainty: Survey and research potentials," European Journal of Operational Research, Elsevier, vol. 165(2), pages 289-306, September.
    5. Janny M. Y. Leung & Guoqing Zhang & Xiaoguang Yang & Raymond Mak & Kokin Lam, 2004. "Optimal Cyclic Multi-Hoist Scheduling: A Mixed Integer Programming Approach," Operations Research, INFORMS, vol. 52(6), pages 965-976, December.
    6. Y N Sotskov & A Allahverdi & T-C Lai, 2004. "Flowshop scheduling problem to minimize total completion time with random and bounded processing times," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(3), pages 277-286, March.
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    Cited by:

    1. De Santis, Marianna & Grani, Giorgio & Palagi, Laura, 2020. "Branching with hyperplanes in the criterion space: The frontier partitioner algorithm for biobjective integer programming," European Journal of Operational Research, Elsevier, vol. 283(1), pages 57-69.
    2. Delorme, Xavier & Dolgui, Alexandre & Kovalev, Sergey & Kovalyov, Mikhail Y., 2019. "Minimizing the number of workers in a paced mixed-model assembly line," European Journal of Operational Research, Elsevier, vol. 272(1), pages 188-194.
    3. Feng, Jianguang & Che, Ada & Chu, Chengbin & Levner, Eugene & Kats, Vladimir, 2024. "Scheduling robotic cells with fixed processing times or time windows: Classification, solution approaches, polynomial algorithms and complexity," European Journal of Operational Research, Elsevier, vol. 319(2), pages 468-483.
    4. Fatemi-Anaraki, Soroush & Tavakkoli-Moghaddam, Reza & Foumani, Mehdi & Vahedi-Nouri, Behdin, 2023. "Scheduling of Multi-Robot Job Shop Systems in Dynamic Environments: Mixed-Integer Linear Programming and Constraint Programming Approaches," Omega, Elsevier, vol. 115(C).

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