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A branch-and-cut algorithm for the discrete (r∣p)-centroid problem

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  • Roboredo, Marcos Costa
  • Pessoa, Artur Alves

Abstract

The environment of the (r∣p)-centroid problem is composed of two noncooperative firms, a leader and a follower, competing to serve the demand of customers from a given market. The demand of each customer is totally served by a facility of the leader or follower according to a customer choice rule. The goal of both the leader and the follower is to maximize its own market share. The (r∣p)-centroid problem consists of deciding where the leader should place p facilities knowing that the follower will react by placing r facilities. The discrete version of the problem is a ∑2p-hard one, where both the applicant facilities and the customers are nodes on a graph. In spite of it, we present an integer programming formulation with polynomially many variables and exponentially many constraints. Moreover, we report several experiments with different number of customers and applicant facilities and different values of p and r. Our results show that our method requires less computational time than the two exact algorithms found in the literature, being able to optimally solve 29 previously open instances with up to 100 customers, 100 applicant facilities and p=r=15.

Suggested Citation

  • Roboredo, Marcos Costa & Pessoa, Artur Alves, 2013. "A branch-and-cut algorithm for the discrete (r∣p)-centroid problem," European Journal of Operational Research, Elsevier, vol. 224(1), pages 101-109.
    • Handle: RePEc:eee:ejores:v:224:y:2013:i:1:p:101-109
    DOI: 10.1016/j.ejor.2012.07.042
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    Cited by:

    1. Gentile, José & Alves Pessoa, Artur & Poss, Michael & Costa Roboredo, Marcos, 2018. "Integer programming formulations for three sequential discrete competitive location problems with foresight," European Journal of Operational Research, Elsevier, vol. 265(3), pages 872-881.
    2. Eligius M. T. Hendrix, 2016. "On competition in a Stackelberg location-design model with deterministic supplier choice," Annals of Operations Research, Springer, vol. 246(1), pages 19-30, November.
    3. Dolores R. Santos-Peñate & Clara M. Campos-Rodríguez & José A. Moreno-Pérez, 2020. "A Kernel Search Matheuristic to Solve The Discrete Leader-Follower Location Problem," Networks and Spatial Economics, Springer, vol. 20(1), pages 73-98, March.
    4. Ekaterina Alekseeva & Yury Kochetov & Alexandr Plyasunov, 2015. "An exact method for the discrete $$(r|p)$$ ( r | p ) -centroid problem," Journal of Global Optimization, Springer, vol. 63(3), pages 445-460, November.
    5. Zhang, Ying & Snyder, Lawrence V. & Ralphs, Ted K. & Xue, Zhaojie, 2016. "The competitive facility location problem under disruption risks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 453-473.
    6. Ivan Davydov & Yury Kochetov & Alexandr Plyasunov, 2014. "On the complexity of the (r|p)-centroid problem in the plane," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 614-623, July.
    7. Marcos Costa Roboredo & Luiz Aizemberg & Artur Alves Pessoa, 2019. "An exact approach for the r-interdiction covering problem with fortification," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(1), pages 111-131, March.
    8. Florensa, Carlos & Garcia-Herreros, Pablo & Misra, Pratik & Arslan, Erdem & Mehta, Sanjay & Grossmann, Ignacio E., 2017. "Capacity planning with competitive decision-makers: Trilevel MILP formulation, degeneracy, and solution approaches," European Journal of Operational Research, Elsevier, vol. 262(2), pages 449-463.

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