A Solution Method to Facility Location Problems using Fuzzy c-Means Clustering and Entropy Maximization Principle

Abstract

A facility location problem is to find a location minimizing the sum of distances between demand points and facility points. If the optimal point should be selected from among the demand points, the problem is called the p-median problem. If the optimal point can be selected arbitrarily from a given domain, the problem is called the Weber problem. The p-median problem is a kind of combinatorial optimization problem. In this paper, a new heuristic algorithm for the p-median problem is proposed. Usually, enumeration methods should be avoided in case of such combinatorial optimization because the combinatorial explosion arises. It is, however, applicable for this problem if the nearest demand points to the optimal point can be specified. Proposed algorithm uses fuzzy c-means clustering for selecting some demand points considered to be near to the optimal points. Further, partial enumeration is done from selected points. In addition, the entropy maximization principle is used for adjusting locations of points for effective enumeration. There are some existing algorithms for Weber problem. This paper gives comparisons with these existing algorithms. In particular, the proposed algorithm has superiority over these existing algorithms for middle size p-median problems.