Multi-level uncapacitated facility location problem with clients' preferences

Stefan MiÅ¡ković, Olivera StanÄ ić, Zorica Stanimirović and Raca Todosijević

European Journal of Industrial Engineering, 2025, vol. 20, issue 4, 569-589

Abstract: This paper introduces the multi-level uncapacitated facility location problem with clients' preferences (MLUFLP-CP), which represents a generalisation of the well-known multi-level uncapacitated facility location problem (MLUFLP). The MLUFLP-CP is first modelled as a bi-level mathematical program, and then reformulated into four equivalent integer linear programs. Due to the NP-hardness of the MLUFLP-CP, the problem instances of real-world dimensions are unsolved to optimality by CPLEX solver. Therefore, we have designed a general variable neighbourhood search (GVNS) metaheuristic as an efficient solution approach to the MLUFLP-CP. The GVNS concept and its parameters are adapted to the multi-level nature of problem, and a novel VND variant, denoted as multi-level VND, is used as a local search improvement procedure. Computational experiments on MLUFLP-CP instances show that the proposed GVNS quickly reaches all known optimal solutions, improves upper bounds obtained by CPLEX and efficiently provides solutions for large-scale instances that were out of reach for CPLEX. [Submitted: 29 March 2024; Accepted: 4 December 2024]

Keywords: multi-level facility location problem; clients' preferences; bi-level mathematical program; integer linear programming; CPLEX solver; variable neighbourhood search; VNS; variable neighbourhood descent; VND. (search for similar items in EconPapers)
Date: 2025
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