SDP-based Benders decomposition for solving p-median quadratic facility location problems

The p-median facility location problem involves selecting the locations for p facilities from a set of potential locations, to balance the trade-off between facility establishment costs and distance to end users. In this paper, we introduce an extension, named the p-median quadratic facility locatio...

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Vydáno v:Computers & operations research Ročník 182; s. 107119
Hlavní autoři: Yang, Yingying, Bui, Hoa T., Loxton, Ryan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.10.2025
Témata:
Benders decomposition
Binary quadratic programming
Facility location problem
Semi-definite programming
Binary quadratic programming
Facility location problem
Benders decomposition
Semi-definite programming
ISSN:0305-0548
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Shrnutí:The p-median facility location problem involves selecting the locations for p facilities from a set of potential locations, to balance the trade-off between facility establishment costs and distance to end users. In this paper, we introduce an extension, named the p-median quadratic facility location problem, that also considers inter-facility distance—important in applications where the facilities serve as intermediate hubs linking sites in different regions. This creates a quadratic term in the objective that makes the problem nonlinear. We develop a Benders decomposition method that uses a tight semi-definite programming relaxation of the Benders master problem, instead of solving the nonlinear master problem directly. We incorporate this decomposition strategy into a branch and bound framework to ensure convergence. Our numerical results show that this method outperforms the linear reformulation and classical Benders decomposition techniques, working independently or in tandem. •A quadratic facility location model for facilities that serve as intermediate hubs.•An algorithm based on Benders decomposition and semi-definite programming relaxation.•Semi-definite programming provides tight relaxations for the master problem.•New algorithm outperforms linearization and classical Benders decomposition.
ISSN:0305-0548
DOI:10.1016/j.cor.2025.107119