Title: Location decisions under facility disruptions in general multi-reliability facility location problem

Authors: Abdulrahman R. Alenezi; Razan W. Alenezi

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

Abstract: In this study, we integrated facility location decisions with reliability considerations and selected the appropriate level of reliability. Specifically, we consider a set of demand points that are to be served by a set of vulnerable facilities. Facilities can be located at various candidate sites with different levels of reliability. Different failure rates and fixed costs determine these levels. The main goal of this study was to investigate the impact of facility disruption on location decisions. The problem was formulated as a linear integer program and solved using two independent approaches: a Lagrangian relaxation (LR) procedure and a simulated annealing (SA) metaheuristic. Findings indicate that the costs associated with locating facilities with different reliability levels follow a linear function rather than being fixed. In addition, the conditions under which specific reliability levels are not included in the optimal solution was identified. These analytical results were validated using a case example.

Keywords: supply chain; facility location problem; reliable supply chain; Lagrangian relaxation; LR; decisions analysis.

DOI: 10.1504/IJAOM.2026.155518

International Journal of Advanced Operations Management, 2026 Vol.17 No.3, pp.327 - 359

Received: 09 Feb 2025
Accepted: 08 Dec 2025
Published online: 04 Aug 2026 *

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