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Double bound method for solving the $$p$$-center location problem. (English) Zbl 1348.90384
Summary: We give a review of existing methods for solving the absolute and vertex restricted $$p$$-center problems on networks and propose a new integer programming formulation, a tightened version of this formulation and a new method based on successive restrictions of the new formulation. A specialization of the new method with two-element restrictions obtains the optimal $$p$$-center solution by solving a series of simple structured integer programs in recognition form. This specialization is called the double bound method. A relaxation of the proposed formulation gives the tightest known lower bound in the literature (obtained earlier by S. Elloumi et al. [INFORMS J. Comput. 16, No. 1, 84–94 (2004; Zbl 1239.90103)]). A polynomial time algorithm is presented to compute this bound. New lower and upper bounds are proposed. Problems from the OR-Library and TSPLIB are solved by the proposed algorithms with up to 3038 nodes. Previous computational results were restricted to networks with at most 1817 nodes.

##### MSC:
 90B80 Discrete location and assignment 05C12 Distance in graphs
##### Software:
OR-Library; CPLEX; TSPLIB
Full Text:
##### References:
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