Optimal Location of Emergency Service Centres Using the Set Covering Location Problem with Multiple Coverage (SCLP-MC): A Case Study of the Libyan Iron and Steel Company

Abstract

This study aims to improve the distribution of emergency service centres within the Libyan Iron and Steel Company by applying the Set Covering Location Problem with Multiple Coverage (SCLP-MC) model. The model seeks to determine the minimum number of service centre locations (p) required to cover a set of demand points (n), while ensuring the achievement of a multiple coverage level (k) for all company facilities within a predefined maximum response time (tmax). The proposed model enhances the reliability of the emergency response system by providing backup coverage that ensures service continuity in situations involving simultaneous incidents or requiring the intervention of multiple service centres to handle large-scale events. The study utilizes accurate spatial data of the company’s facilities, including geographic coordinates and travel times between locations based on the internal road network. The mathematical model was formulated using Binary Integer Linear Programming (BILP) to determine the optimal number of service centres (p) that satisfy the double-coverage requirement (k = 2) within the specified maximum response time (tmax = 3 minutes). The model was solved using the Excel Solver tool. The results revealed that the optimal number of emergency service centers is five (p = 5), ensuring double coverage for all 37 company facilities within the specified response time. The coverage analysis further indicated that 12 facilities achieved the basic coverage level provided by two centres, while 15 facilities received triple coverage, and 10 facilities achieved the highest coverage level through four service centres. These findings confirm the effectiveness of the SCLP-MC model in improving the spatial planning of emergency service centres and supporting decision-making processes aimed at enhancing safety levels and operational efficiency in industrial facilities.