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Cooperative Game Theory Based Coordinated Scheduling of Two-Machine Flow-Shop and Transportation

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Abstract

A cooperative game theoretical approach is taken to production and transportation coordinated scheduling problems of two-machine flow-shop (TFS-PTCS problems) with an interstage transporter. The authors assume that there is an initial scheduling order for processing jobs on the machines. The cooperative sequencing game models associated with TFS-PTCS problems are established with jobs as players and the maximal cost savings of a coalition as its value. The properties of cooperative games under two different types of admissible rearrangements are analysed. For TFS-PTCS problems with identical processing time, it is proved that, the corresponding games are σ0-component additive and convex under one admissible rearrangement. The Shapley value gives a core allocation, and is provided in a computable form. Under the other admissible rearrangement, the games neither need to be σ0-component additive nor convex, and an allocation rule of modified Shapley value is designed. The properties of the cooperative games are analysed by a counterexample for general problems.

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References

  1. Lee C Y and Strusevich V A, Two-machine shop scheduling with an uncapacitated interstage transporter, IIE Transactions, 2005, 37(8): 725–736.

    Article  Google Scholar 

  2. Gong H and Tang L X, Two-machine flowshop scheduling with intermediate transportation under job physical space consideration, Computers & Operations Research, 2011, 38(9): 1267–1274.

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhong W Y and Chen Z L, Flowshop scheduling with interstage job transportation, Journal of Scheduling, 2015, 18(4): 411–422.

    Article  MathSciNet  MATH  Google Scholar 

  4. Dong J M, Wang X S, Hu J L, et al., An improved two-machine flowshop scheduling with intermediate transportation, Journal of Combinatorial Optimization, 2016, 31(3): 1316–1334.

    Article  MathSciNet  MATH  Google Scholar 

  5. Yuan S P, Li T K, and Wang B L, A discrete differential evolution algorithm for flow shop group scheduling problem with sequence-dependent setup and transportation times, Journal of Intelligent Manufacturing, 2021, 32(2): 427–439.

    Article  Google Scholar 

  6. Xin X, Jiang Q Q, Li S H, et al., Energy-efficient scheduling for a permutation flow shop with variable transportation time using an improved discrete whale swarm optimization, Journal of Cleaner Production, 2021, 293(5): 126121.

    Article  Google Scholar 

  7. Lei C J, Zhao N, Ye S, et al., Memetic algorithm for solving flexible flow-shop scheduling problems with dynamic transport waiting times, Computers & Industrial Engineering, 2020, 139: 105984.

    Article  Google Scholar 

  8. Wei Q, Kang L Y, and Shan E F, Batching scheduling in a two-level supply chain with earliness and tardiness penalties, Journal of Systems Science & Complexity, 2016, 29(2): 478–498.

    Article  MathSciNet  MATH  Google Scholar 

  9. Cai S and Liu K, Heuristics for online scheduling on identical parallel machines with two GoS levels, Journal of Systems Science & Complexity, 2019, 32(4): 1180–1193.

    Article  MathSciNet  MATH  Google Scholar 

  10. Curiel I, Pederzoli G, and Tijs S, Sequencing games, European Journal of Operational Research, 1989, 40(3): 344–351.

    Article  MathSciNet  MATH  Google Scholar 

  11. Zhou Y P and Gu X S, One machine sequencing game with lateness penalties, International Journal on Information, 2012, 15(11): 4429–4434.

    MathSciNet  MATH  Google Scholar 

  12. Ji M, Liu S, Zhang X L, et al., Sequencing games with slack due windows and group technology considerations, Journal of the Operational Research Society, 2017, 68(2): 121–133.

    Article  Google Scholar 

  13. Li F and Yang Y, Cooperation in a single-machine scheduling problem with job deterioration, Proceedings of THE 2016 IEEE Information Technology, Networking, Electronic and Automation Control Conference, Chongqing, 2016, 20–22.

  14. Yang G J, Sun H, and Uetz M, Cooperative sequencing games with position-dependent learning effect, Operations Research Letters, 2020, 48(4): 428–434.

    Article  MathSciNet  MATH  Google Scholar 

  15. Velzen B V, Sequencing games with controllable processing times, European Journal of Operational Research, 2006, 172(1): 64–85.

    Article  MathSciNet  MATH  Google Scholar 

  16. Lohmann E, Borm P, and Slikker M, Sequencing situations with just-in-time arrival, and related games, Mathematical Methods of Operations Research, 2014, 80(3): 285–305.

    Article  MathSciNet  MATH  Google Scholar 

  17. Saavedra-Nieves A, Schouten J, and Borm P, On interactive sequencing situations with exponential cost functions, European Journal of Operational Research, 2020, 280(1): 78–89.

    Article  MathSciNet  MATH  Google Scholar 

  18. Schouten J, Saavedra-Nieves A, and Fiestras-Janeiro M G, Sequencing situations and games with non-linear cost functions under optimal order consistency, European Journal of Operational Research, 2021, 294(2): 734–745.

    Article  MathSciNet  MATH  Google Scholar 

  19. Liu Z X, Lu L, and Qi X T, Cost allocation in rescheduling with machine unavailable period, European Journal of Operational Research, 2018, 266(1): 16–28.

    Article  MathSciNet  MATH  Google Scholar 

  20. Yang G J, Sun H, Hou D S, et al., Games in sequencing situations with externalities, European Journal of Operational Research, 2019, 278(2): 699–708.

    Article  MathSciNet  MATH  Google Scholar 

  21. Musegaas M, Borm P, and Quant M, Step out-step in sequencing games, European Journal of Operational Research, 2015, 246(3): 894–906.

    Article  MathSciNet  MATH  Google Scholar 

  22. Musegaas M, Borm P, and Quant M, On the convexity of step out-step in sequencing games, TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, 26: 68–109.

    MathSciNet  MATH  Google Scholar 

  23. Slikker M, Balancedness of sequencing games with multiple parallel machines, Annals of Operations Research, 2005, 137(1): 177–189.

    Article  MathSciNet  MATH  Google Scholar 

  24. Ciftci B, Borm P, Hamers H, et al., Batch sequencing and cooperation, Journal of Scheduling, 2008, 16(4): 405–415.

    Article  MathSciNet  MATH  Google Scholar 

  25. Curiel I, Multi-stage sequencing situations, International Journal of Game Theory, 2010, 39(1): 151–162.

    Article  MathSciNet  MATH  Google Scholar 

  26. Curiel I, Compensation rules for multi-stage sequencing games, Annals Operations Research, 2015, 225(1): 65–82.

    Article  MathSciNet  MATH  Google Scholar 

  27. Sun W J, Gong H, Xu K, et al., Cooperative games on proportionate flow-shop scheduling problem with due-dates, Control and Decision, 2022, 37(3): 712–720.

    Google Scholar 

  28. Atay A, Calleja P, and Soteras S, Open shop scheduling games, European Journal of Operational Research, 2021, 295(1): 12–21.

    Article  MathSciNet  MATH  Google Scholar 

  29. Klijn F and Sánchez E, Sequencing games without initial order, Mathematical Methods of Operations Research, 2006, 63(1): 53–62.

    Article  MathSciNet  MATH  Google Scholar 

  30. Le Breton M, Owen G, and Weber S, Strongly balanced cooperative games, International Journal of Game Theory, 1992, 20(4): 419–427.

    Article  MathSciNet  MATH  Google Scholar 

  31. Borm P, Fiestras-Janeiro G, Hamers H, et al., On the convexity of games corresponding to sequencing situations with due dates, European Journal of Operational Research, 2002, 136(3): 616–634.

    Article  MathSciNet  MATH  Google Scholar 

  32. Shapley L S, Cores of convex games, International Journal of Game Theory, 1971, 1(1): 11–26.

    Article  MathSciNet  MATH  Google Scholar 

  33. Shapley L S, A value for n-person games, Annals of Mathematics Studies, 1953, 28: 307–317.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Management, Shenyang University of Technology, Shenyang, 110870, China

    Wenjuan Sun, Hua Gong & Peng Liu

  2. Liaoning Key Laboratory of Intelligent Optimization and Control for Ordnance Industry, School of Science, Shenyang Ligong University, Shenyang, 110159, China

    Wenjuan Sun & Hua Gong

Authors
  1. Wenjuan Sun
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  2. Hua Gong
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  3. Peng Liu
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Corresponding author

Correspondence to Hua Gong.

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The authors declare no conflict of interest.

Additional information

This research was supported in part by the Liaoning Province Xingliao Talents Plan Project under Grant No. XLYC2006017, and in part by the Scientific Research Funds Project of Educational Department of Liaoning Province under Grant Nos. LG202025 and LJKZ0260.

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Sun, W., Gong, H. & Liu, P. Cooperative Game Theory Based Coordinated Scheduling of Two-Machine Flow-Shop and Transportation. J Syst Sci Complex 36, 2415–2433 (2023). https://doi.org/10.1007/s11424-023-2491-3

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  • DOI: https://doi.org/10.1007/s11424-023-2491-3

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