A hybrid method for planning and scheduling

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A hybrid method for planning and scheduling (2004)

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by J. N. Hooker

Venue:	In Procs. of the 10th Intern. Conference on Principles and Practice of Constraint Programming - CP 2004
Citations:	44 - 7 self

BibTeX

@INPROCEEDINGS{Hooker04ahybrid,
    author = {J. N. Hooker},
    title = {A hybrid method for planning and scheduling},
    booktitle = {In Procs. of the 10th Intern. Conference on Principles and Practice of Constraint Programming - CP 2004},
    year = {2004},
    pages = {305--316},
    publisher = {Springer}
}

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Abstract

We combine mixed integer linear programming (MILP) and constraint programming (CP) to solve 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 minimum cost problems, as well as minimum makespan problems in which all tasks have the same release date and deadline. We obtain computational speedups of several orders of magnitude relative to the state of the art in both MILP and CP. We address a fundamental class of planning and scheduling problems for manufacturing and supply chain management. Tasks must be assigned to facilities and scheduled subject to release dates and deadlines. Tasks may run in parallel on a given facility provided the total resource consumption at any time remains with limits (cumulative scheduling). In our study the objective is to minimize cost or minimize makespan. The problem naturally decomposes into an assignment portion and a scheduling portion. We exploit the relative strengths of mixed integer linear programming (MILP) and constraint programming (CP) by applying MILP to the assignment problem and CP to the scheduling problem. We then link the two with a logic-based Benders algorithm. We obtain speedups of several orders of magnitude relative to the existing state of the art in both mixed integer programming (CPLEX) and constraint programming (ILOG Scheduler). As a result we solve larger instances to optimality than could be solved previously. In minimum makespan problems, the Benders method provides a feasible solution and a lower bound on the optimal makespan even when it is terminated before finding a provably optimal solution. 1. The Basic Idea Benders decomposition solves a problem by enumerating values of certain primary variables. For each set of values enumerated, it solves the subproblem that results from fixing the primary variables to these values. Solution of the subproblem generates a Benders cut (a type of nogood) that the primary variables must satisfy in all subsequent solutions enumerated. The next set of values for the primary variables is

Keyphrases

primary variable hybrid method scheduling problem constraint programming magnitude relative minimum makespan problem mixed integer linear programming cumulative scheduling several order relative strength optimal solution certain primary variable ilog scheduler computational speedup feasible solution subsequent solution supply chain management fundamental class logic-based bender decomposition resource constraint assignment problem release date next set scheduling portion bender method minimum cost problem parallel subject assignment portion mixed integer programming logic-based bender algorithm total resource consumption optimal makespan basic idea bender decomposition

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