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Decomposition Techniques for Hybrid MILP/CP Models applied to Scheduling and Routing Problems

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Book cover Hybrid Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 45))

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Abstract

This chapter provides a review of decomposition algorithms for models that are formulated as hybrid mixed-integer linear/constraint programming problems, such as logic Bender Decomposition and Constraint Programming-Based Column Generation. We first focus the decomposition techniques on single stage scheduling problems with parallel machines where the hybrid model provides a natural representation as the decisions decompose into assignment and sequencing decisions. We describe a general decomposition algorithm for the hybrid MILP/CP model in terms of a Benders decomposition scheme, as well as in terms of a branch and cut framework. We then consider Vehicle Routing and Crew Rostering applications to illustrate how Hybrid Branch-and-Price method can be applied, and we discuss the different models that have been proposed in the literature.

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Authors and Affiliations

  1. Laboratório Nacional de Energiae Geologia, Unidade de Modelação e Optimização de Sistemas Energéticos, 1649-038, Lisboa, Portugal

    Pedro M. Castro

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  1. Pedro M. Castro
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  2. Ignacio E. Grossmann
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  3. Louis-Martin Rousseau
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Correspondence to Pedro M. Castro .

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  1. , Department of Computer Science, Brown University, Providence, 02912, Rhode Island, USA

    Pascal van Hentenryck

  2. , Department of Electronics, Computer Scie, Università di Bologna, Viale Risorgimento 2, Bologna, 40136, Italy

    Michela Milano

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Castro, P.M., Grossmann, I.E., Rousseau, LM. (2011). Decomposition Techniques for Hybrid MILP/CP Models applied to Scheduling and Routing Problems. In: van Hentenryck, P., Milano, M. (eds) Hybrid Optimization. Springer Optimization and Its Applications, vol 45. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1644-0_4

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