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Planning and Scheduling by Logic-Based Benders Decomposition

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  • J. N. Hooker

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

Abstract

We combine mixed-integer linear programming (MILP) and constraint programming (CP) to solve an important class of planning and scheduling problems. Tasks are allocated to facilities using MILP and scheduled using CP, and the two are linked via logic-based Benders decomposition. Tasks assigned to a facility may run in parallel subject to resource constraints (cumulative scheduling). We solve problems in which the objective is to minimize cost, makespan, or total tardiness. We obtain significant computational speedups, of several orders of magnitude for the first two objectives, relative to the state of the art in both MILP and CP. We also obtain better solutions and bounds for problems than cannot be solved to optimality.

Suggested Citation

  • J. N. Hooker, 2007. "Planning and Scheduling by Logic-Based Benders Decomposition," Operations Research, INFORMS, vol. 55(3), pages 588-602, June.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:3:p:588-602
    DOI: 10.1287/opre.1060.0371
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    References listed on IDEAS

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    1. Vipul Jain & Ignacio E. Grossmann, 2001. "Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 13(4), pages 258-276, November.
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