An Evolutionary Algorithm for the Leader-Follower Facility Location Problem with Proportional Customer Behavior

Biesinger, Benjamin; Hu, Bin; Raidl, Günther R.

doi:10.1007/978-3-319-09584-4_19

Cited by 7 publications

(10 citation statements)

References 17 publications

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“…A local search procedure, combined with the archive into a tabu search variant, further improves promising solutions of the EA and thus turns it into a powerful hybrid approach. This article extends our previous work [5] by covering all customer behavior scenarios introduced in [24] and providing models as well as numerical results.…”

Section: Demand Modelmentioning

confidence: 82%

“…The objective function for the follower's problem (4) maximizes the follower's turnover. Similarly as in the leader's problem, (5) ensures that the follower places exactly r facilities. Inequalities (6) together with the objective function ensure the u j variables to be set correctly, i.e., decide for each customer j ∈ J from which competitor he is served.…”

Section: Binary Essentialmentioning

confidence: 98%

“…The algorithmic framework is also used in [6] for binary customer behavior and in [5] for proportional customer behavior, both only considered essential demand. We use an incomplete solution representation only storing the facilities of the leader indicated by the binary vector x = (x 1 , .…”

Section: Evolutionary Algorithmmentioning

confidence: 99%

“…The definitions for the binary essential case is taken from [6] and for the proportional case from [5]. In the following let (X, Y ) be a candidate solution to our competitive facility location problem, where X ⊆ I, |X| = p, is the set of locations chosen by the leader and Y ⊆ I, |Y | = r, is the associated set of follower locations.…”

Section: Problem Definitionmentioning

confidence: 99%

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Models and algorithms for competitive facility location problems with different customer behavior

Biesinger

Raidl

2015

Ann Math Artif Intell

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Competitive facility location problems arise in the context of two noncooperating companies, a leader and a follower, competing for market share from a given set of customers. We assume that the firms place a given number of facilities on locations taken from a discrete set of possible points. For this bi-level optimization problem we consider six different customer behavior scenarios from the literature: binary, proportional and partially binary, each combined with essential and unessential demand. The decision making for the leader and the follower depends on these scenarios. In this work we present mixed integer linear programming models for the follower problem of each scenario and use them in combination with an evolutionary algorithm to optimize the location selection for the leader. A complete solution archive is used to detect already visited candidate solutions and convert them efficiently into similar, not yet considered ones. We present numerical results of our algorithm and compare them to so far state-of-the-art approaches from the literature. Our method shows good performance in all customer behavior scenarios and is able to outperform previous solution procedures on many occasions.

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Section: Demand Modelmentioning

confidence: 82%

Section: Binary Essentialmentioning

confidence: 98%

Section: Evolutionary Algorithmmentioning

confidence: 99%

Section: Problem Definitionmentioning

confidence: 99%

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Models and algorithms for competitive facility location problems with different customer behavior

Biesinger

Raidl

2015

Ann Math Artif Intell

Self Cite

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“…Ramezanian and Ashtiani (2011) solved the same problem via an exact solution method. Biesinger et al (2014b) presented an evolutionary algorithm with an embedded tabu search to solve the same problem. A complete solution archive has been used to detect already visited candidate solutions and convert them into not yet considered ones.…”

Section: Models With Inelastic Demandmentioning

confidence: 99%

Competitive location: a state-of-art review

Ashtiani¹

2016

10.5267/j.ijiec

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This paper provides a review on recent works in the field of competitive facility location models based on the following seven components: 1) Variables, 2) Competition type, 3) Solution space, 4) Customer behavior, 5) Demand type, 6) Number of new facilities and 7) Relocation and redesign possibility. First, the components are introduced and then based on these components; different studies are compared with each other via a proposed taxonomy and finally a review on work of each paper is provided.

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Bilevel Models on the Competitive Facility Location Problem

Aras

Küçükaydın

2017

Springer Optimization and Its Applications

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Facility location and allocation problems have been a major area of research for decades, which has led to a vast and still growing literature. Although there are many variants of these problems, there exist two common features: finding the best locations for one or more facilities and allocating demand points to these facilities. A considerable number of studies assume a monopolistic viewpoint and formulate a mathematical model to optimize an objective function of a single decision maker. In contrast, competitive facility location (CFL) problem is based on the premise that there exist competition in the market among different firms. When one of the competing firms acts as the leader and the other firm, called the follower, reacts to the decision of the leader, a sequential-entry CFL problem is obtained, which gives rise to a Stackelberg type of game between two players. A successful and widely applied framework to formulate this type of CFL problems is bilevel programming (BP). In this chapter, the literature on BP models for CFL problems is reviewed, existing works are categorized with respect to defined criteria, and information is provided for each work.

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An Evolutionary Algorithm for the Leader-Follower Facility Location Problem with Proportional Customer Behavior

Cited by 7 publications

References 17 publications

Models and algorithms for competitive facility location problems with different customer behavior

Models and algorithms for competitive facility location problems with different customer behavior

Competitive location: a state-of-art review

Bilevel Models on the Competitive Facility Location Problem

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