international journal of production economics ELSEVIER Int. J. Production Economics 35 (1994) 373-377 Supply centers allocation under budget restrictions minimizing the longest delivery time C. Tsouros*, M. Satratzemi University ?f zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA M acedonia, Department of Applied Iqformatics. 156 Egnatias Str. 54621 Thessaloniki, Grww Abstract Let G = (V, E) be a connected directed graph expressing a distribution network. The elements of D G k’ represent demand centers, while S c V contains the candidate supply centers. To each node x ES, we associate a weight w(x) which corresponds to the cost of installing a supply center at node x. To every arc (x, y) E E we associate a weight a( x, y) which indicates the required time to reach node y directly from node x. The purpose of this paper is the determination of the subsets of S under a given budget restriction, so to minimize the longest delivery time of facilities to the demand nodes of D. 1. Introduction The location of industrial plants, hospitals, fire stations, parks, electric power plants, etc., has become an important consideration in today’s society. Increased demands for public services, low budget, increased costs and more competition have stressed the importance of the optimal location of both public and private facilities. Thus the problem of finding the “best” locations of supply centers in networks, emerges in many practical situations and has many variations, depending on the considered parameters and criterions, which are closely related to the type of the provided facilities [l, 21. Such a practical problem is the finding of the optimal location of emergency services or warehouses * Corresponding author. which maintain sensitive products. In this case the objective is to minimize the largest distance be- tween the demand and supply centers. In this paper we suppose that each candidate supply center loca- tion is associated to a given cost, that might be the corresponding land cost and/or the cost to con- struct and equip it. The distances between all pairs of locations in the examined domain are given. In this paper we develop a method which finds the subset(s) of supply centers locations the total cost of which does not exceed a given budget and which minimizes the longest distance between the supply and demand centers. The next section is devoted to the necessary definitions and notations. The proposed procedure minimize longest distance (MLD) is developed in Section 3. An analytical numerical example is presented in Section 4, while Section 5 comprises the epilogue. 0925-5273/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved. SSDI 0925-5273(93)E0143-J