Introduction: Location problems seek to determine the best locations for facilities with respect to various objective functions and constraints. In most real-world problems with congested demand structure, a demand node has to wait for service if its assigned facility is busy with serving other demands. Such situations are generally observed in emergency services such as medical, ambulance, or police operations, in which minutes, or even seconds are important to provide a successful service to demands. Therefore, to increase the quality of service, decision-makers aim to provide multiple-coverage for each demand, i.e. ensure a backup supply, in congested networks. In this research, we use simulation to study the performance of location models when the concept of backup supply is implemented when designing the location schemes. In particular, we consider the three well-known location models, viz. p-median problem, maximal coverage location problem, and p-center problem, and analyze the pros & cons of each model with respect to multiple assessment criteria under backup coverage requirement. The p-median problem aims to minimize the total (weighted) distance or travel time between demands and their nearest facilities. The maximal coverage location problem, on the other hand, seeks to maximize the total (weighted) number of demand nodes covered. In this formulation it is assumed that a demand is covered only if it lies within a specific range of a facility. Finally, the p-center problem attempts to minimize the maximum distance (or travel time) between demands and their nearest facilities. Purpose: The purpose of this research is to analyze the impact of backup service requirement on the performance of the three well-known location models when different performance metrics are considered. Scope: The scope of this study includes the p-median problem, maximal coverage location problem, and p-center problem, and all simulation runs are performed using randomly generated demand and location data. The research has lasted approximately four months. Limitations: This research only considers deterministic demand and resource data and does not incorporate any type of uncertainty. Method: To achieve our objectives, we first modified the location models such that they can incorporate the backup coverage concept. Next, we performed extensive Monte Carlo simulation runs using randomly generated demand and location data and assessed the performance of each model with respect to different criteria. In simulations runs we generated problem settings with varying facility coverage ranges and backup requirement levels. Each problem setting is solved for 100 random replications. Instances are generated and solved in the General Algebraic Modeling System (GAMS©) environment using CPLEX 22.214.171.124 solver. Findings: The simulation results provided us with the quantitative performances of each location model with respect to multiple assessment criteria. The results revealed that, on the overall, the p-median approach is superior to other two approaches in terms of most of the performance metrics. As expected, it is outperformed by the maximal coverage location problem approach when the objectives include the minimization of the maximum distance to primary and/or backup facilities is desired. We also observed that the maximal coverage location problem approach is best for maximizing the amount of demand nodes covered by both primary and backup coverage or by at least the primary coverage when the coverage range is short. Conclusion: The results obtained through the extensive Monte Carlo simulation runs provided us with a quantitative assessment of the performances of the three well-known location models with respect to multiple metrics. Our analysis revealed that the most appropriate type and structure of a location model varies significantly depending on the objective of the decision maker as well as the requirement on the backup coverage level. Hence, in cases where multiple metrics are important for planners, the results obtained in this study can be a powerful guide in deciding to implement a location model and backup coverage level which can increase the efficiency and the service quality of a location design.
Anahtar Kelimeler: Location Planning, Backup Coverage, Simulation, p-Median Problem, Maximal Coverage Location Problem; p-Center Problem.