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

• Published in: Annals of operations research Vol. 335; no. 1; pp. 385 - 424
• Main Authors: Tang, Luohao, Wu, Dexiang
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2024; Springer Nature B.V
• Subjects: Account management; Algorithms; Business and Management; Combinatorics; Customer services; Customers; Integer programming; Mixed integer; Operations research; Operations Research/Decision Theory; Original Research; Site selection; Theory of Computation; Local search; Mental accounting; Risk management; Lagrangian relaxation; Single source constraint; Capacitated facility location problem
• ISSN: 0254-5330; 1572-9338
• DOI: 10.1007/s10479-023-05572-3

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.