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Enhanced capacitated facility location problem for mental accounting management using partial resource concentration

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Abstract

This paper studies a framework of Reliable Capacitated Facility Location Problem with Single source constraint, which allows us to capture the mental account management problem for a bank under uncertain environment. In the problem, each facility, corresponding to a financial product, has limited capacity and may fail randomly, which represents that the product fails to reach the threshold level of return. Each customer, corresponding to a mental account, is served by a single primary facility or product, and its demands, or the setting goals, can be split on several backup facilities or alternative investments with redundant capacity. With the operation, a portion of the satisfaction can still be met by the backup facilities when the primary service of a customer fails. We formulate a mixed integer programming model for the problem and design a Lagrangian relaxation based solution algorithm, which sophisticatedly exploits the structure of the model and transfers the complicated relaxation problems into 0–1 knapsack problems to reduce the complexity. A local search procedure is also incorporated into the algorithm to enhance the accuracy of small- and large-scale computation. Finally, a real-life case of mental accounting is investigated to illustrate the application of the decision model.

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Acknowledgements

This paper was supported in part by the National Natural Science Foundation of China under Grant 72021001 and in part by China Scholarship Council and in part by the Fundamental Research Funds for the Central Universities. This work was supported in part by the National Natural Science Foundation of China under Grant 72210107001.

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  1. College of Systems Engineering, National University of Defense Technology, Changsha, China

    Luohao Tang

  2. School of Economics and Management, Beihang University, Beijing, 100191, China

    Dexiang Wu

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  1. Luohao Tang
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Tang, L., Wu, D. Enhanced capacitated facility location problem for mental accounting management using partial resource concentration. Ann Oper Res 335, 385–424 (2024). https://doi.org/10.1007/s10479-023-05572-3

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