Abstract
We consider a geographical region with spatially separated customers, whose demand is currently served by some pre-existing facilities owned by different firms. An entering firm wants to compete for this market locating some new facilities. Trying to guarantee a future satisfactory captured demand for each new facility, the firm imposes a constraint over its possible locations (a finite set of candidates): a new facility will be opened only if a minimal market share is captured in the short-term. To check that, it is necessary to know the exact captured demand by each new facility. It is supposed that customers follow the partially binary choice rule to satisfy its demand. If there are several new facilities with maximal attraction for a customer, we consider that the proportion of demand captured by the entering firm will be equally distributed among such facilities (equity-based rule). This ties breaking rule involves that we will deal with a nonlinear constrained discrete competitive facility location problem. Moreover, minimal attraction conditions for customers and distances approximated by intervals have been incorporated to deal with a more realistic model. To solve this nonlinear model, we first linearize the model, which allows to solve small size problems because of its complexity, and then, for bigger size problems, a heuristic algorithm is proposed, which could also be used to solve other constrained problems.
Highlights
IntroductionWe consider a certain geographical area in which customers are supposed to be concentrated in demand points (see Francis et al, 2002)
When a new firm wants to enter this market with the idea of capturing as much demand as possible, the company is facing a problem of Competitive Location
A new discrete location model is proposed where i) partially binary choice rule is applied to customers, ii) real distances are approximated by intervals of different ranges, iii) minimum attraction conditions have been considered for each customer, iv) an equity-based rule has been used in case of ties in maximum attraction between facilities, and v) minimal market share constraints are introduced to the new facilities unsure of a future captured demand
Summary
We consider a certain geographical area in which customers are supposed to be concentrated in demand points (see Francis et al, 2002). In this paper we are going to consider that customers follow the partially binary or multideterministic rule, where it is supposed that several firms are present in the market with some pre-existing facilities, and the full demand of a customer is served by all the firms but patronizing only one facility from each firm, the facility with the maximum attraction, its demand is split between those facilities proportionally with their attraction (see Fernández et al, 2017; Hakimi, 1990; Suárez-Vega et al, 2004). A new discrete location model is proposed where i) partially binary choice rule is applied to customers, ii) real distances are approximated by intervals of different ranges, iii) minimum attraction conditions have been considered for each customer, iv) an equity-based rule has been used in case of ties in maximum attraction between facilities, and v) minimal market share constraints are introduced to the new facilities unsure of a future captured demand.
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