Issue 16, March 2007

Selected Papers of EWGLA12

**Contents**

- R.
SUáREZ-VEGA, P. DORTA-GONZáLEZ, D.R. SANTOS-PEñATE
The (

**r**|**X**_{p})-medianoid model for non-essential services and proportional preferences with attraction functions**Abstract**Most of the competitive location problems assume essential services, which means that the total demand is allocated to the facilities operating in the market. This is a reasonable assumption for first order goods but not for services such as restaurants or cinemas which can be unused by consumers if, for example, the travel distance is large or the quality is low, in such a way that the demand is not totally satisfied.

In this paper the (r|X

_{p})-medianoid problem for non-essential services and proportional preferences incorporating attraction functions is studied. It is an extension of the results presented by Hakimi (1990) for non-essential demands and proportional customer preferences. In his work, Hakimi uses distance as the only preference criterion and maximizes the market share. In this paper, distance is combined with the attractiveness of the facilities to define the customer preference and the objective is to maximize profits. A node optimality result, more general than the node optimality theorem presented by Hakimi, is proved. - T.CáCERES, J.A.MESA, J.L.PINO
Behaviour of equality measures for facility location on a vertex of a general network

**Abstract**An empirical study of thirteen equality measures for the location of a facility on a vertex of a general network regarding vertex demand is carried out. In order to group those measures with similar behaviour, four similarity gauges are applied. In each of the three resulting groups, the utilization of one function instead of another from the same set leads to acceptable results.

**Keywords**: Equality; Facility Location. - M. DIMOPOULOU, I. GIANNIKOS
The effects of variations of the demand space definition on demand covering models

**Abstract**Demand covering problems deal with the proper location of servers as either to minimize the number of servers needed to cover a given demand space or to maximize coverage of the demand space given a number of available servers. Different local conditions within the demand space affect the determination of demand points and influence the optimality of the coverage.

In the present study, we examine how the optimal solution of the demand covering problems is affected by variations in the distribution of the demand points. A number of different definitions of demand points are developed using Geographical Information Systems techniques. A heuristic is then developed to further explore and improve different variations of a first solution with respect to a number of secondary objectives.

**Key words**: Demand Covering, Facility Location, Geographical Information Systems - P. DORTA-GONZáLEZ, D.R.
SANTOS-PEñATE, R. SUáREZ-VEGA
Location-price equilibrium on trees for a duopoly with negative externality

**Abstract**This paper presents a location-price equilibrium problem on a tree. Nash equilibrium conditions are presented for a spatial competition model that incorporates price, transport and externality costs. The presented result describes a sufficient condition under which the Nash equilibria on locations and prices are guaranteed. Moreover, the Nash equilibrium on location is a median of the tree. An example is then given to show that there are medians that are not Nash equilibria.

**Key words**: duopoly, location, price, externality, equilibrium. - H.HENNES, H.W.HAMACHER
Integrated scheduling and location models: single machine makespan problems

**Abstract**Scheduling and location models are often used to tackle problems in production, logistics, and supply chain management. Instead of treating these models independent of each other, as is usually done in the literature, we consider in this paper an integrated model in which the locations of machines define release times for jobs. Polynomial solution algorithms are presented for single machine problems in which the scheduling part can be solved by the earliest release time rule.

**Key words.**Location problems, scheduling theory.

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On 27 Apr 2007, 16:22.