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The p-Median Problem

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Book cover Cell Formation in Industrial Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 79))

Abstract

This chapter focuses on the p-median problem (PMP) and its properties. We consider a pseudo-Boolean formulation of the PMP, demonstrate its advantages and derive the most compact MILP formulation for the PMP within the class of mixed-Boolean linear programming formulations. Further, we develop two applications of the pseudo-Boolean approach: a construction of PMP instances that are expected to be complex for any solution algorithm and a definition of an equivalence relation for PMP instances. By equivalence we mean that solving one instance gives a solution for all the instances from its equivalence class. The proposed equivalence relation can be extended to any other problem modelled via the PMP, for example, the cell formation problem.

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Notes

  1. 1.

    MINLEAF is a polynomial-time algorithm and is essentially based on finding the maximum cardinality matching.

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Authors and Affiliations

  1. Department of Operations, University of Groningen, Groningen, The Netherlands

    Boris Goldengorin

  2. Department of Industrial and Systems Engineering, University of Gainesville, Gainesville, FL, USA

    Boris Goldengorin & Panos M. Pardalos

  3. University of Groningen, Groningen, The Netherlands

    Dmitry Krushinsky

Authors
  1. Boris Goldengorin
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  2. Dmitry Krushinsky
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  3. Panos M. Pardalos
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Goldengorin, B., Krushinsky, D., Pardalos, P.M. (2013). The p-Median Problem. In: Cell Formation in Industrial Engineering. Springer Optimization and Its Applications, vol 79. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8002-0_2

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