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The branch and cut method for the facility location problem with client’s preferences


Numerical study is provided of the methods for solving the facility location problem when the clients choose some suppliers by their own preferences. Various formulations of this problem as an integer linear programming problem are considered. The authors implement a cutting plane method based on the earlier proposed family of valid inequalities which arises from connection with the problem for a pair of matrices. The results of numerical experiment are presented for testing this method. An optimal solution is obtained by the two versions of the branch and cut method with the suggested cutting plane method. The simulated annealing method is proposed for obtaining the upper bounds of the optimal solution used in exact methods. Numerical experiment approves the efficiency of the implemented approach in comparison with the previously available methods.

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Correspondence to I. L. Vasilyev.

Additional information

Original Russian Text © I.L. Vasilyev, K.B. Klimentova, 2009, published in Diskretnyi Analiz i Issledovanie Operatsii, 2009, Vol. 16, No. 2, pp. 21–41.

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Vasilyev, I.L., Klimentova, K.B. The branch and cut method for the facility location problem with client’s preferences. J. Appl. Ind. Math. 4, 441–454 (2010).

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Key words

  • facility location problem with client’s preferences
  • cutting plane method
  • local search
  • branch and cut method