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The multilevel facility location and pricing problems: the computational complexity and the stability analysis

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Abstract

We consider Stackelberg games and corresponding bilevel and trilevel programming models based on facility location and pricing processes. At the upper level of the bilevel models, the company decides on the location of its uncapacitated facilities and the assignment of optimal prices for homogeneous products. In the trilevel models, two companies compete for client demand by making decisions sequentially. We have established the dependence of the computational complexity of the problems under study on the choice of pricing policy and the concept of facility allocation. We have divided the problems into three classes: polynomially solvable, NP-hard, and \(\Sigma ^P_2\)-hard. Moreover, the problems of stability analysis are discussed in conclusion.

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Acknowledgements

This work has been supported by the Grant of the Russian Science Foundation, RSF-ANR 21-41-09017.

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  1. Laboratory of Mathematical Models of Decision Making, Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, Novosibirsk, Novosibirsk Region, Russia, 630090

    Artem A. Panin & Alexandr V. Plyasunov

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  1. Artem A. Panin
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Panin, A.A., Plyasunov, A.V. The multilevel facility location and pricing problems: the computational complexity and the stability analysis. Optim Lett 17, 1295–1315 (2023). https://doi.org/10.1007/s11590-022-01924-3

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