Title: A multi-reliability facility location problem

Authors: Razan W. Alenezi; Abdulrahman R. Alenezi

Addresses: Department of Industrial and Management Systems Engineering, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, 13060, Safat, Kuwait ' Department of Industrial and Management Systems Engineering, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, 13060, Safat, Kuwait

Abstract: In this paper, we considered a fixed charge facility location with multiple reliability problems. Specifically, a supply chain consisting of a single product set of candidate distribution centres, and set of demand points. Distribution centres are prone to failure; therefore, each demand point must be assigned to both primary and secondary facilities. Besides, at each candidate site, different facility reliability levels can be defined. Each reliability level has a different failure rate and is associated with a different fixed cost. We formulated the model as a large-scale linear integer program. In order for the solution procedure to be achievable, the model complexity was reduced by adding redundant constraints. This resulted in a size reduction up to 98.1%. Finally, lower and upper bounds on the optimal solution were developed using the Lagrangian relaxation procedure. The results confirmed that the solution was 1% within the optimal solution.

Keywords: supply chain; facility location problem; facility reliability; Lagrangian relaxation.

DOI: 10.1504/IJLSM.2026.155668

International Journal of Logistics Systems and Management, 2026 Vol.54 No.4, pp.453 - 482

Received: 05 Dec 2023
Accepted: 01 Jan 2024
Published online: 10 Aug 2026 *

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