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Solving a Truck Dispatching Scheduling Problem Using Branch-and-Cut

Author

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  • Robert E. Bixby

    (Rice University, Houston, Texas)

  • Eva K. Lee

    (Georgia Institute of Technology, Atlanta, Georgia)

Abstract

A branch-and-cut IP solver is developed for a class of structured 0/1 integer programs arising from a truck dispatching scheduling problem. This problem involves a special class of knapsack equality constraints. Families of facets for the polytopes associated with individual knapsack constraints are identified. In addition, a notion of “conflict graph” is utilized to obtain an approximating node-packing polytope for the convex hull of all 0/1 solutions. The branch-and-cut solver generates cuts based on both the knapsack equality constraints and the approximating node-packing polytope, and incorporates these cuts into a tree-search algorithm that uses problem reformulation and linear programming-based heuristics at each node in the search tree to assist in the solution process. Numerical experiments are performed on large-scale real instances supplied by Texaco Trading & Transportation, Inc. The optimal schedules correspond to cost savings for the company and greater job satisfaction for drivers due to more balanced work schedules and income distribution.

Suggested Citation

  • Robert E. Bixby & Eva K. Lee, 1998. "Solving a Truck Dispatching Scheduling Problem Using Branch-and-Cut," Operations Research, INFORMS, vol. 46(3), pages 355-367, June.
  • Handle: RePEc:inm:oropre:v:46:y:1998:i:3:p:355-367
    DOI: 10.1287/opre.46.3.355
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    References listed on IDEAS

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    1. Laurence A. Wolsey, 1976. "Technical Note—Facets and Strong Valid Inequalities for Integer Programs," Operations Research, INFORMS, vol. 24(2), pages 367-372, April.
    2. Karla L. Hoffman & Manfred Padberg, 1993. "Solving Airline Crew Scheduling Problems by Branch-and-Cut," Management Science, INFORMS, vol. 39(6), pages 657-682, June.
    3. Harlan Crowder & Ellis L. Johnson & Manfred Padberg, 1983. "Solving Large-Scale Zero-One Linear Programming Problems," Operations Research, INFORMS, vol. 31(5), pages 803-834, October.
    4. WOLSEY, Laurence A., 1976. "Facets and strong valid inequalities for integer programs," LIDAM Reprints CORE 246, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Karla L. Hoffman & Manfred Padberg, 1991. "Improving LP-Representations of Zero-One Linear Programs for Branch-and-Cut," INFORMS Journal on Computing, INFORMS, vol. 3(2), pages 121-134, May.
    6. Ellis L. Johnson & Michael M. Kostreva & Uwe H. Suhl, 1985. "Solving 0-1 Integer Programming Problems Arising from Large Scale Planning Models," Operations Research, INFORMS, vol. 33(4), pages 803-819, August.
    7. M. Padberg & G. Rinaldi, 1989. "A Branch-and-Cut Approach to a Traveling Salesman Problem with Side Constraints," Management Science, INFORMS, vol. 35(11), pages 1393-1412, November.
    8. WOLSEY, Laurence A., 1976. "Further facet generating procedures for vertex packing polytopes," LIDAM Reprints CORE 278, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Lawrence D. Bodin, 1990. "Twenty Years of Routing and Scheduling," Operations Research, INFORMS, vol. 38(4), pages 571-579, August.
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    Cited by:

    1. Escudero, L. F. & Munoz, S., 2003. "On identifying dominant cliques," European Journal of Operational Research, Elsevier, vol. 149(1), pages 65-76, August.

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