Abstract
In this research, a maximal covering location problem (MCLP) with real-world constraints such as multiple types of facilities and vehicles with different setup costs is taken into account. An original mixed integer linear programming (MILP) model is constructed in order to find the optimal solution. Since the problem at hand is shown to be NP-hard, a constructive heuristic method and a meta-heuristic approach based on genetic algorithm (GA) are developed to solve the problem. To find the most effective solution technique, a set of problems of different sizes is randomly generated and solved by the proposed solution methods. Computational results demonstrate that the heuristic method is capable of producing optimal or near-optimal solutions in a rational execution time.
Highlights
Finding facility location is a long time frame strategic decision for companies
The Covering problem (CP) is composed of two main classifications: set-covering problem (SCP) and maximal covering location problem (MCLP) (Schilling et al, 1993)
The objective of the SCP, first introduced by Toregas et al (1971), is to find the minimum number of facilities so that all demand points are satisfied within a standard time or distance
Summary
Finding facility location is a long time frame strategic decision for companies. it is considered as a decisive constituent in companies' strategic planning. Pirkul & Schilling (1989) developed a mathematical model for the capacitated MCLP (CMCLP) with workload capacities on facilities and the allocation of multiple levels of backup or prioritized service for all demand points They proposed a solution technique based on Lagrangian relaxation to solve the problem. The objective function of his first model was only set to maximize the total covered demand under capacity constraints, whereas the objective function of his second proposed model was set to maximize the weighted coverage and minimize the average distance from the uncovered demands to the located facilities He developed two heuristic approaches based on the Greedy adding algorithm and Lagrangian relaxation to solve the problems.
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