Two exact algorithms for the capacitated p-median problem

Abstract.

The p-median problem has been widely studied in combinatorial optimisation, but its generalisation to the capacitated case has not. We propose a branch and price algorithm, comparing it with a standard MIP solver and a branch and bound algorithm based on Lagrangean relaxation. We present computational experience, using test instances drawn from the literature and new instances with higher ratio between the number of medians p and the number of nodes N. The branch and price algorithm shows very good performances and computational time robustness in solving problems for any \(\frac{p}{N}\) ratio.

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Correspondence to Alberto Ceselli.

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Received: December 2002, Revised: August 2003

AMS classification:

90C10, 90C27

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Ceselli, A. Two exact algorithms for the capacitated p-median problem. 4OR 1, 319–340 (2003). https://doi.org/10.1007/s10288-003-0023-5

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Keywords:

  • Location theory
  • Lagrangean relaxation
  • column generation
  • branch and bound