Polyhedral study of the capacitated vehicle routing problem View Full Text


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Article Info

DATE

1993-06

AUTHORS

Gerard Cornuejols, Farid Harche

ABSTRACT

The capacitated vehicle routing problem (CVRP) considered in this paper occurs when goods must be delivered from a central depot to clients with known demands, usingk vehicles of fixed capacity. Each client must be assigned to exactly one of the vehicles. The set of clients assigned to each vehicle must satisfy the capacity constraint. The goal is to minimize the total distance traveled. When the capacity of the vehicles is large enough, this problem reduces to the famous traveling salesman problem (TSP). A variant of the problem in which each client is visited by at least one vehicle, called the graphical vehicle routing problem (GVRP), is also considered in this paper and used as a relaxation of CVRP. Our approach for CVRP and GVRP is to extend the polyhedral results known for TSP. For example, the subtour elimination constraints can be generalized to facets of both CVRP and GVRP. Interesting classes of facets arise as a generalization of the comb inequalities, depending on whether the depot is in a handle, a tooth, both or neither. We report on the optimal solution of two problem instances by a cutting plane algorithm that only uses inequalities from the above classes. More... »

PAGES

21-52

References to SciGraph publications

  • 1979-12. On the symmetric travelling salesman problem I: Inequalities in MATHEMATICAL PROGRAMMING
  • 2009-02-24. On the symmetric travelling salesman problem: Solution of a 120-city problem in COMBINATORIAL OPTIMIZATION
  • 1976-06. An Integer Programming Approach to the Vehicle Scheduling Problem in JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY
  • 2009-02-24. On the symmetric travelling salesman problem: A computational study in COMBINATORIAL OPTIMIZATION
  • 1985-09. The traveling salesman problem on a graph and some related integer polyhedra in MATHEMATICAL PROGRAMMING
  • 1973-12. Edmonds polytopes and weakly hamiltonian graphs in MATHEMATICAL PROGRAMMING
  • 1969-09. An Algorithm for the Vehicle-dispatching Problem in JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY
  • 1988-01. A new class of cutting planes for the symmetric travelling salesman problem in MATHEMATICAL PROGRAMMING
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/bf01580599

    DOI

    http://dx.doi.org/10.1007/bf01580599

    DIMENSIONS

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    133 https://www.grid.ac/institutes/grid.147455.6 schema:alternateName Carnegie Mellon University
    134 schema:name Graduate School of Industrial Administration, Carnegie Mellon University, Schenley Park, 15213-3890, Pittsburgh, PA, USA
    135 rdf:type schema:Organization
     




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