ArticleJournal of heuristics2026
Mathematical formulations and a Relax-and-Fix heuristic algorithm for capacitated reliable fixed-charge facility location problems.
Article in Journal of heuristics, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
The reliable fixed-charge facility location problem extends the fixed-cost facility location problem by incorporating facility unreliability. This paper addresses a novel capacitated version of the reliable fixed-charge facility location problem, where the failure probability of each facility is site-dependent, differing from existing literature models. Additionally, facilities are assumed to have limited capacity for demand allocation, with the option to increase capacity to a predetermined value in case of supply chain disruptions. To solve this problem, we develop a non-linear mixed-integer programming formulation and present its linear version. Given the NP-hard nature of the problem, we propose a novel Relax-and-Fix heuristic for its solution. We evaluate the efficiency of the proposed algorithm by solving a variety of experimental instances with different network sizes. Results demonstrate that the Relax-and-Fix heuristic improves upper bounds for problem instances and achieves this within a shorter computational time. Furthermore, sensitivity analysis is conducted on capacity and failure probabilities, and relevant results are presented.
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