An integrated method for planning and scheduling to minimize tardiness.

*(English)*Zbl 1103.68811Summary: We combine Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) to minimize tardiness in planning and scheduling. Tasks are allocated to facilities using MILP and scheduled using CP, and the two are linked via logic-based Benders decomposition. We consider two objectives: minimizing the number of late tasks, and minimizing total tardiness. Our main theoretical contribution is a relaxation of the cumulative scheduling subproblem, which is critical to performance. We obtain substantial computational speedups relative to the state of the art in both MILP and CP. We also obtain much better solutions for problems that cannot be solved to optimality.

##### MSC:

68T20 | Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) |

90B35 | Deterministic scheduling theory in operations research |

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\textit{J. N. Hooker}, Constraints 11, No. 2--3, 139--157 (2006; Zbl 1103.68811)

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##### References:

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