Abstract
In the k-level facility location problem with penalties, each client will be either serviced or rejected completely. And if the client is planned to be serviced, then it must be connected to a sequence of k different kinds of facilities located in k levels of hierarchy. The total cost including the facility cost, connection cost and penalty cost will be jointly paid by all the clients. In the corresponding game of the k-level facility location problem with penalties, called the k-level facility location game with penalties, the total cost should be allocated to different clients. This work set out a cost-sharing scheme for the k-level facility location game with penalties that is cross-monotonic, competitive, and the approximate cost recovery is 6.
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This research was supported by the National Natural Science Foundation of China (Nos. 11901544 and 11801251).
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Wang, FM., Wang, JJ., Li, N. et al. A Cost-Sharing Scheme for the k-Level Facility Location Game with Penalties. J. Oper. Res. Soc. China 10, 173–182 (2022). https://doi.org/10.1007/s40305-021-00345-w
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DOI: https://doi.org/10.1007/s40305-021-00345-w