Modeling and solution of maximal covering problem considering gradual coverage with variable radius over multi-periods

Facility location is a critical component of strategic planning for public and private firms. Due to high cost of facility location, making decisions for such a problem has become an important issue which have gained a large deal of attention from researchers. This study examined the gradual maximal covering location problem with variable radius over multiple time periods. In gradual covering location problem, it is assumed that full coverage is replaced by a coverage function, so that increasing the distance from the facility decreases the amount of demand coverage. In variable radius covering problems, however, each facility is considered to have a fixed cost along with a variable cost which has a direct impact on the coverage radius. In real-world problems, since demand may change over time, necessitating relocation of the facilities, the problem can be formulated over multiple time periods. In this study, a mixed integer programming model was presented in which not only facility capacity was considered, but also two objectives were followed: coverage maximization and relocation cost minimization. A metaheuristic algorithm was presented to solve the maximal covering location problem. A simulated annealing algorithm was proposed, with its results presented. Computational results and comparisons demonstrated good performance of the simulated annealing algorithm.