Pierre Hanjoul

A comparison of two dual-based procedures for solving the p-median problem

Abstract We compare two dual-based procedures for solving the p -median problem. They rely upon alternative Lagrangean relaxations of the problem. We describe the algorithms and report on our computational experiments.

A facility location problem with clients' preference orderings

Abstract The Simple Plant Location Problem (SPLP) consists in identifying a pattern of facilities among a set of potential sites so that the sum of the costs for opening the facilities and for supplying a group of geographically dispersed clients therefrom is minimized. It is posited in this framework that the locator rules on the allocation of the clients to the facilities. When the clients are free to decide upon which facility they will attend, their choices do not necessarily match the most economical supply pattern from the point of view of the locator. We suppose here that each client has a preference ordering on the list of potential sites whereby he determines his allocation out of any set of open facilities. This preference ordering depends on characteristics of the client, of the sites, and of the trip between the clients location and the sites. Mathematically, we translate the orderings into a set of constraints to be appended to the SPLP. This new problem, termed SPLPO, has a wide range of applications as shown by a series of examples. We present an algorithm for solving the SPLPO and extensive computational experiments are reported.

Simple plant location under uniform delivered pricing

Abstract Given a geographical system of demand functions, the simple-plant location problem under uniform delivered pricing consists in determining the delivered price taken as uniform for all customers, the number, the locations, the sizes and the market areas of the plants which supply these customers, in order to maximize the profit of the firm. A model is proposed, which allows, moreover, to integrate some aspects of the commercial policy of the firm, i.e., its decision to satisfy all markets with positive demands or profitable markets only, or to allow a maximum unit loss or require a minimum unit gain on each served market. An efficient algorithm is presented and illustrated by an example. Computational results with a code using recursively Erlenkotters DUALOC program as a subroutine are summarized.

Elements of planar analysis in spatial competition

Abstract The spatial competition in price and location between firms has traditionally been analyzed on a one-dimensional space and with linear transportation costs. The present paper attempts at studying that problem on the plane if transportation costs are a strictly increasing fumction of Euclidean distance.

The location of a firm on a network

Since the pioneering work of Launhardt and Weber (1909), the location theory of the firm has developed from a particular model of the firm in which the location decision criterion is the minimisation of transportation costs.1 Actually it is not surprising that this model, called hereafter Weberian, still is the basic reference in the field in spite of its difference with the neo-classical model of the firm. One has only to remember the minor position held by spatial economics in the mainstream economics over several decades.2 Despite appearances, this theoreticl hiatus is of no serious consequences for the study of location problems. Indeed, the Weberian model now appears to be a short-cut leading to the neo-classical model. The argument is simple and it will be used in several propositions of this chapter: a place which maximises the profit of the firm at the same time minimises the transportation cost included in the profit.3 Consequently, the characteristics of the Weberian model solution remain valid for the neo-classical model solution. This explains why, in some parts of the chapter, we follow the lines of proofs given elsewhere. Unfortunately, there are exceptions to that equivalence rule which, not surprisingly, correspond to location problems which are not easy to deal with from both the theoretical and numerical points of view. Such a problem is discussed in section 3.

Les aires théoriques de marché des villes

Le but de cet article est de donner quelques proprietes generales des aires theoriques de marche des villes. On montre notamment comment la forme des aires de marche change avec la fonction de cout de transport utilisee. Diverses autres proprietes sont donnees concernant les bornes topologiques des aires de marche ainsi que les conditions auxquelles ces aires sont vides, bornees, convexes.