A multi-objective facility location problem in the presence of variable gradual coverage performance and cooperative cover

This paper presents a multi-objective facility location problem which includes facilities with gradual covering decay, cooperative demand coverage and variable coverage performance. The objectives include minimizing deviations from demand coverage level requirements, allocated budget, and facility capacities. The gradual coverage performance, variable facility costs and facility capacities are considered as non-linear functions. The location problem is first modeled as a multi-objective integer non-linear program (INLP). Next, after mapping the problem to a network-like structure, an equivalent multi-objective integer linear program (ILP) is developed. With the objective of attaining high-quality solutions within reasonable computing times, we propose a combined INLP-ILP solution procedure. Extensive computational experiments are taken on randomly generated data for small, medium and large-sized problems. The detailed results are provided, and the combined INLP-ILP procedure is shown to be efficient.