Solving a Huff-like competitive location and design model for profit maximization in the plane

Fernández, José María Pérez; Pelegrı́n, Blas; Plastria, Frank; G.-Tóth, Boglárka

doi:10.1016/j.ejor.2006.02.005

Cited by 116 publications

(118 citation statements)

References 40 publications

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“…On the other hand, a typical form for design cost might be P l k¼1 e q k q 0 þq 1 À e q 1 ; q 0 [ 0 and q 1 , given values (Fernández et al 2007). We note that the number of facilities to be located is not fixed; its value is to be determined by the solution of the model.…”

Section: Proposed Modelmentioning

confidence: 99%

“…On the other hand, several researchers are recently interested in the studies and models in which their aim is to find the optimal design and location of new facilities (Plastria and Carrizosa 2004;Aboolian et al 2007;Fernández et al 2007;Tóth et al 2009;Redondo et al 2009;Redondo et al 2011;Saiz et al 2011;Saidani et al 2012;Wang and Ouyang 2013;Redondo et al 2013). These problems are called location-design models in competitive location literature and both the optimal location and design of new facilities are considered as the variables of the problem.…”

Section: Introductionmentioning

confidence: 99%

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A firefly algorithm for solving competitive location-design problem: a case study

et al. 2016

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This paper aims at determining the optimal number of new facilities besides specifying both the optimal location and design level of them under the budget constraint in a competitive environment by a novel hybrid continuous and discrete firefly algorithm. A real-world application of locating new chain stores in the city of Tehran, Iran, is used and the results are analyzed. In addition, several examples have been solved to evaluate the efficiency of the proposed model and algorithm. The results demonstrate that the performed method provides good-quality results for the test problems.

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Section: Proposed Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A firefly algorithm for solving competitive location-design problem: a case study

et al. 2016

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“…As studied by Fernández et al (2007), we are dealing with a global optimisation problem; see Fig. 1, which shows the multimodal behaviour of problem (F P(x 1 )).…”

Section: Indicesmentioning

confidence: 99%

“…In Drezner and Drezner (2004) and Fernández et al (2007), procedures are given to maximise the market share captured by a given chain when the facility locations of the competitors are fixed as in problem (F P(x 1 )). As studied by Fernández et al (2007), we are dealing with a global optimisation problem; see Fig.…”

Section: Indicesmentioning

confidence: 99%

On a branch-and-bound approach for a Huff-like Stackelberg location problem

et al. 2008

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Modelling the location decision of two competing firms that intend to build a new facility in a planar market can be done by a Huff-like Stackelberg location problem. In a Huff-like model, the market share captured by a firm is given by a gravity model determined by distance calculations to facilities. In a Stackelberg model, the leader is the firm that locates first and takes into account the actions of the competing chain (follower) locating a new facility after the leader. The follower problem is known to be a hard global optimisation problem. The leader problem is even harder, since the leader has to decide on location given the optimal action of the follower. So far, in literature only heuristic approaches have been tested to solve the leader problem. Our research question is to solve the leader problem rigorously in the sense of having a guarantee on the reached accuracy. To answer this question, we develop a branch-and-bound approach. Essentially, the bounding is based on the zero sum concept: what is gain for one chain is loss for the other. We also discuss several ways of creating bounds for the underlying (follower) sub-problems, and show their performance for numerical cases.

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“…Now let us focus on the (1|1)-centroid locationdesign problem in the plane with deterministic supplier choice. Fernández et al (2007) analyse first the second level optimisation of Π(x, a) over a continuous quality parameter a when location x is fixed. They show that for the classical Huff model with convex investment cost this implies a concave problem.…”

Section: Introductionmentioning

confidence: 99%

On competition in a Stackelberg location-design model with deterministic supplier choice

Hendrix

2015

Ann Oper Res

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We study a market situation where two firms maximize market capture by deciding on the location in the plane and investing in a competing quality against investment cost. Clients choose one of the suppliers; i.e. deterministic supplier choice. To study this situation, a game theoretic model is formulated. We show that for the modelled situation no Nash equilibrium exists. However, a so-called Stackelberg equilibrium, where one of the firms (the leader) is aware of what the other (follower) is going to do, exists. The questions under study is whether co-location is a natural phenomenon in this case and in which situation one of the firms is not entering the market. The study requires a multi-level thinking where the decisions on location follow from the known quality investment behavior and the actions of the leader take the decisions of the follower into account.

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Solving a Huff-like competitive location and design model for profit maximization in the plane

Cited by 116 publications

References 40 publications

A firefly algorithm for solving competitive location-design problem: a case study

A firefly algorithm for solving competitive location-design problem: a case study

On a branch-and-bound approach for a Huff-like Stackelberg location problem

On competition in a Stackelberg location-design model with deterministic supplier choice

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