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The traveling salesman problem with pickup and delivery: polyhedral results and a branch-and-cut algorithm

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Abstract

The Traveling Salesman Problem with Pickup and Delivery (TSPPD) is defined on a graph containing pickup and delivery vertices between which there exists a one-to-one relationship. The problem consists of determining a minimum cost tour such that each pickup vertex is visited before its corresponding delivery vertex. In this paper, the TSPPD is modeled as an integer linear program and its polyhedral structure is analyzed. In particular, the dimension of the TSPPD polytope is determined and several valid inequalities, some of which are facet defining, are introduced. Separation procedures and a branch-and-cut algorithm are developed. Computational results show that the algorithm is capable of solving to optimality instances involving up to 35 pickup and delivery requests, thus more than doubling the previous record of 15.

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Authors and Affiliations

  1. School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, 2052, Australia

    Irina Dumitrescu

  2. Canada Research Chair in Distribution Management, HEC Montréal, 3000, chemin de la Côte-Sainte-Catherine, Montréal, H3T 2A7, Canada

    Stefan Ropke & Gilbert Laporte

  3. Canada Research Chair in Logistics and Transportation, HEC Montréal, 3000, chemin de la Côte-Sainte-Catherine, Montréal, H3T 2A7, Canada

    Jean-François Cordeau

Authors
  1. Irina Dumitrescu
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  2. Stefan Ropke
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  3. Jean-François Cordeau
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  4. Gilbert Laporte
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Correspondence to Stefan Ropke.

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Dumitrescu, I., Ropke, S., Cordeau, JF. et al. The traveling salesman problem with pickup and delivery: polyhedral results and a branch-and-cut algorithm. Math. Program. 121, 269–305 (2010). https://doi.org/10.1007/s10107-008-0234-9

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  • DOI: https://doi.org/10.1007/s10107-008-0234-9

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