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Cooperative maximum-flow problem under uncertainty in logistic networks

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  • Hafezalkotob, Ashkan
  • Makui, Ahmad

Abstract

Many decision-making problems in the context of transhipment and logistics, distribution networks, airline planning and so on, can best be analyzed by the means of maximum-flow models in networks. In a multiple-owner network, several players possess arcs and nodes of a network. Since parameters of the network in many real problems are highly uncertain, maintaining a stable flow is as much important as maximizing the flow passing through the network. Thus, a key question is how the independent owners of a network should collaborate to maintain a reliable maximum flow. We address this question by presenting a stochastic mathematical programming model for the multiple-owner graph problem under uncertainty. Afterwards, a number of collaboration methods are studied based on the game theory. These methods are illustrated with an example to gain an insight into properties of the corresponding game results and behavior of the different solution concepts.

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  • Hafezalkotob, Ashkan & Makui, Ahmad, 2015. "Cooperative maximum-flow problem under uncertainty in logistic networks," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 593-604.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:593-604
    DOI: 10.1016/j.amc.2014.10.080
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    1. Rodica Branzei & Dinko Dimitrov & Stef Tijs, 2008. "Models in Cooperative Game Theory," Springer Books, Springer, edition 0, number 978-3-540-77954-4, July.
    2. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    3. Ehud Kalai & Eitan Zemel, 1982. "Totally Balanced Games and Games of Flow," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 476-478, August.
    4. Ehud Kalai & Eitan Zemel, 1982. "Generalized Network Problems Yielding Totally Balanced Games," Operations Research, INFORMS, vol. 30(5), pages 998-1008, October.
    5. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    6. Gregory D. Glockner & George L. Nemhauser, 2000. "A Dynamic Network Flow Problem with Uncertain arc Capacities: Formulation and Problem Structure," Operations Research, INFORMS, vol. 48(2), pages 233-242, April.
    7. Xiao, Tiaojun & Yang, Danqin, 2008. "Price and service competition of supply chains with risk-averse retailers under demand uncertainty," International Journal of Production Economics, Elsevier, vol. 114(1), pages 187-200, July.
    8. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    9. Bar-Shira, Ziv & Finkelshtain, Israel, 1999. "Two-moments decision models and utility-representable preferences," Journal of Economic Behavior & Organization, Elsevier, vol. 38(2), pages 237-244, February.
    10. Frisk, M. & Göthe-Lundgren, M. & Jörnsten, K. & Rönnqvist, M., 2010. "Cost allocation in collaborative forest transportation," European Journal of Operational Research, Elsevier, vol. 205(2), pages 448-458, September.
    11. Robert P. Gilles, 2010. "The Cooperative Game Theory of Networks and Hierarchies," Theory and Decision Library C, Springer, number 978-3-642-05282-8, March.
    12. Lozano, S. & Moreno, P. & Adenso-Díaz, B. & Algaba, E., 2013. "Cooperative game theory approach to allocating benefits of horizontal cooperation," European Journal of Operational Research, Elsevier, vol. 229(2), pages 444-452.
    13. John M. Mulvey & Robert J. Vanderbei & Stavros A. Zenios, 1995. "Robust Optimization of Large-Scale Systems," Operations Research, INFORMS, vol. 43(2), pages 264-281, April.
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    Cited by:

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    2. Adil Baykasoğlu & Burcu Kubur Özbel, 2021. "Explicit flow-risk allocation for cooperative maximum flow problems under interval uncertainty," Operational Research, Springer, vol. 21(3), pages 2149-2179, September.
    3. Hafezalkotob, Ashkan, 2017. "Competition, cooperation, and coopetition of green supply chains under regulations on energy saving levels," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 97(C), pages 228-250.
    4. Mehmet Onur Olgun, 2022. "Collaborative airline revenue sharing game with grey demand data," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(3), pages 861-882, September.
    5. Dahlberg, Joen & Göthe-Lundgren, Maud & Engevall, Stefan, 2017. "A note on the nonuniqueness of the Equal Profit Method," Applied Mathematics and Computation, Elsevier, vol. 308(C), pages 84-89.
    6. Mehryar, Mehdi & Hafezalkotob, Ashkan & Azizi, Amir & Sobhani, Farzad Movahedi, 2023. "Dynamic zoning of the network using cooperative transmission and maintenance planning: A solution for sustainability of water distribution networks," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    7. Trust Tawanda & Philimon Nyamugure & Santosh Kumar & Elias Munapo, 2023. "An intelligent node labelling maximum flow algorithm," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(4), pages 1276-1284, August.
    8. Ying Wang & Xiangyu Mao & Hashim Zameer, 2022. "Designing benefit distribution driven innovation strategy for local enterprises under the global value chain system," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(6), pages 2358-2373, September.
    9. Yong Wang & Yingying Yuan & Xiangyang Guan & Haizhong Wang & Yong Liu & Maozeng Xu, 2019. "Collaborative Mechanism for Pickup and Delivery Problems with Heterogeneous Vehicles under Time Windows," Sustainability, MDPI, vol. 11(12), pages 1-30, June.
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