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A tighter continuous time formulation for the cyclic scheduling of a mixed plant

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  • POCHET, Yves

    (Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE))

  • WARICHET, François

Abstract

In this paper, based on the cyclic scheduling formulation of Schilling and Pantelides [22], we propose a continuous time mixed integer linear programming (MILP) formulation for the cyclic scheduling of a mixed plant, i.e. a plant composed of batch and continuous tasks. The cycle duration is a variable of the model and the objective is to maximize productivity. By using strengthening techniques and the analysis of small polytopes related to the problem formulation, we strengthen the initial formulation by tightening some initial constraints and by adding valid inequalities. We show that this strengthened formulation is able to solve moderate size problems quicker than the initial one. However, for real size cases, it remains difficult to obtain the optimal solution of the scheduling problem quickly. Therefore, we introduce MILP-based heuristic methods in order to solve these larger instances, and show that they can provide quite good feasible solutions quickly.

Suggested Citation

  • POCHET, Yves & WARICHET, François, 2007. "A tighter continuous time formulation for the cyclic scheduling of a mixed plant," LIDAM Discussion Papers CORE 2007026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2007026
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    References listed on IDEAS

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    1. Stadtler, Hartmut, 2003. "Multilevel lot sizing with setup times and multiple constrained resources: Internally rolling schedules with lot-sizing windows," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 20204, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    2. Christodoulos Floudas & Xiaoxia Lin, 2005. "Mixed Integer Linear Programming in Process Scheduling: Modeling, Algorithms, and Applications," Annals of Operations Research, Springer, vol. 139(1), pages 131-162, October.
    3. Hartmut Stadtler, 2003. "Multilevel Lot Sizing with Setup Times and Multiple Constrained Resources: Internally Rolling Schedules with Lot-Sizing Windows," Operations Research, INFORMS, vol. 51(3), pages 487-502, June.
    4. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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