The noncooperative fixed charge transportation problem

Sagratella, Simone;Schmidt, Marcel;Sudermann-Merx, Nathan
(2020) European Journal of Operational Research — Vol. 284, n° 1, p. 373-382 (2020)

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  • Sagratella, SimoneDepartment of Computer, Control, and Management Engineering, Sapienza University of Rome, Italy
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  • Schmidt, MarcelUCLouvain
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  • Sudermann-Merx, NathanAdvanced Business Analytics, BASF SE, Germany
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Abstract
We introduce the noncooperative fixed charge transportation problem (NFCTP), which is a game-theoretic extension of the fixed charge transportation problem. In the NFCTP, competing players solve coupled fixed charge transportation problems simultaneously. Three versions of the NFCTP are discussed and compared which differ in the treatment of shared social costs. This may be used from central authorities in order to find a socially balanced framework which is illustrated in a numerical study. Using techniques from generalized Nash equilibrium problems with mixed-integer variables we show the existence of Nash equilibria for these models and examine their structural properties. Since there is no unique equilibrium for the NFCTP, we also discuss how to solve the Nash selection problem and, finally, propose numerical methods for the computation of Nash equilibria which are based on mixed-integer programming.
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Sagratella, S., Schmidt, M., & Sudermann-Merx, N. (2020). The noncooperative fixed charge transportation problem. European Journal of Operational Research, 284(1), 373-382. https://doi.org/10.1016/j.ejor.2019.12.024 (Original work published 2020)