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

  • Roboredo, Marcos Costa
  • Pessoa, Artur Alves
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712005991
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    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 224 (2013)
    Issue (Month): 1 ()
    Pages: 101-109

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    Handle: RePEc:eee:ejores:v:224:y:2013:i:1:p:101-109
    Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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    1. Campos Rodrí­guez, Clara M. & Moreno Pérez, José A., 2008. "Multiple voting location problems," European Journal of Operational Research, Elsevier, vol. 191(2), pages 437-453, December.
    2. Eiselt, H. A. & Laporte, Gilbert, 1997. "Sequential location problems," European Journal of Operational Research, Elsevier, vol. 96(2), pages 217-231, January.
    3. Campos Rodriguez, Clara M. & Moreno Perez, Jose A., 2003. "Relaxation of the Condorcet and Simpson conditions in voting location," European Journal of Operational Research, Elsevier, vol. 145(3), pages 673-683, March.
    4. Eiselt, H. A. & Laporte, G., 1989. "Competitive spatial models," European Journal of Operational Research, Elsevier, vol. 39(3), pages 231-242, April.
    5. Hakimi, S. Louis, 1983. "On locating new facilities in a competitive environment," European Journal of Operational Research, Elsevier, vol. 12(1), pages 29-35, January.
    6. Noltemeier, H. & Spoerhase, J. & Wirth, H.-C., 2007. "Multiple voting location and single voting location on trees," European Journal of Operational Research, Elsevier, vol. 181(2), pages 654-667, September.
    7. Kress, Dominik & Pesch, Erwin, 2012. "Sequential competitive location on networks," European Journal of Operational Research, Elsevier, vol. 217(3), pages 483-499.
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