A fuzzy set covering-clustering algorithm for facility location problem

Mathematical models and solution algorithms which address the problem of locating facilities and allocating customers varies widely in terms of basic assumptions, mathematical complexity and computational performance. In this paper, we are concerned with a problem of locating the number of facilities among a finite number of sites such that all existing sites (customers) are covered by at least one facility. The problem was modeled and solved in three stages. In the first stage, an improved fuzzy set covering solution was proposed to determine the minimum number of facilities. In the second stage, the well known k-means clustering algorithm was applied for demand classification into groups. In the third stage, the assignment model was used to locate facilities in each cluster. Using extensive simulation studies, we also show that the proposed approach performs considerably well in all considered conditions in comparison to classic covering methods.