New exact method to solve multi-capacitated location problem using set partitioning formulation

In this paper, we present one generalization of the famous capacitated p-median location problem, called budget constraint multi-capacitated location problem (MCLP). This generalization is characterized by allowing each facility to be used with different capacity levels. We consider n customers, m facilities and l capacity levels, we note that the solution shape of MCLP can be represented as a set of disjoint clusters, each cluster is composed of one facility and a subset of customers. When creating clusters, some constraints must be met, namely the level selection and capacity. In this work, we present the new formulation of the MCLP based on set partitioning, then we suggest an adapted solving method, which will be called NFF (Nearest Facility First). The NFF approach is used in two ways: as a heuristic by taking only the first solution found or exact method when waiting finish the execution. Computational results are presented at the end using instances that we have created under some criteria of difficulties or adapted from those of p-median problems available in literature. The NFF method provides very good results for low and medium difficulty instances, but it is less effective for the more complex ones. To remedy this problem, the method will be supplemented by column generation approach.