On the conditional p-median problem

Abstract

-In this paper we investigate the conditional p-median problem. Optimal algorithms for the Euclidean case in the plane for the 1-median with several existing facilities are proposed. A general heuristic algorithm for any metric or environment (network or continuous space) is presented. The algorithm is based on solving several p-median problems. I N T R O D U C T I O N A p-median (or p-center) problem is to locate p facilities among customers (demand points) such that customers get their service from the closest facility. The p-median objective is to minimize the sum of weighted distances between the demand points and their closest facility, and the p-center objective is to minimize the maximum among these distances [1, 2]. A p-median (or p-center) problem is called conditional when some existing facilities are already located and the best location for p new facilities to serve a set of demand points is sought. Customers are assumed to get service from the closest facility whether existing or new. The conditional problem seems to be a natural extension of the p-median (or p-center) problems which have many practical applications [1,2]. A conditional model is very common when an expansion of an existing set of service facilities is planned. The conditional version of these problems has received some attention by researchers in recent years [3-9]. We mention Ref. [5] in particular where an efficient method to solve the p-median problem on networks is suggested. The conditional p-median problem is related to competitive location problems discussed in some recent papers [I0-12]. In competitive location problems the new facilities try to attract as much demand as possible from the existing facilities. While in the conditional p-median problem attracting demand points serves to lower the total weighted distances for all the demand points and therefore the demand points get the benefits, in competitive location the purpose of attracting demand points is for the benefit of the new facilities and the benefit to the demand points is not considered in the objective function. tPar t of this research was done while the author was on sabbatical leave at the Department of Management, The Hong Kong University of Science and Technology, Kowloon, Hong Kong. Zvi Drezner is Professor and Chairman, Department of Management Science/Information Systems, California State University-Fullerton. He received his Ph.D. in Computer Science from the Technion, Israel Institute of Technology. His main interests are in location theory, mathematical programming and computational statistics. He has published over eighty papers in journals like Operations Research, Management Science, Naval Research Logistics, Communications #1 Statistics, liE Transactions, and others.

DOI: 10.1016/0305-0548(94)00033-5

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Cite this paper

@article{Drezner1995OnTC, title={On the conditional p-median problem}, author={Zvi Drezner}, journal={Computers & OR}, year={1995}, volume={22}, pages={525-530} }