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Logic-Based Benders Decomposition for Large-Scale Optimization

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Large Scale Optimization in Supply Chains and Smart Manufacturing

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 149))

Abstract

Logic-based Benders decomposition (LBBD) is a substantial generalization of classical Benders decomposition that, in principle, allows the subproblem to be any optimization problem rather than specifically a linear or nonlinear programming problem. It is amenable to a wide variety of large-scale problems that decouple or otherwise simplify when certain decision variables are fixed. This chapter presents the basic theory of LBBD and explains how classical Benders decomposition is a special case. It also describes branch and check, a variant of LBBD that solves the master problem only once. It illustrates in detail how Benders cuts and subproblem relaxations can be developed for some planning and scheduling problems. It then describes the role of LBBD in three large-scale case studies. The chapter concludes with an extensive survey of the LBBD literature, organized by problem domain, to allow the reader to explore how Benders cuts have been developed for a wide range of applications.

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Notes

  1. 1.

    An infeasible problem is viewed as having optimal value ∞ (when minimizing) or −∞ (when maximizing).

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  1. Carnegie Mellon University, Pittsburgh, PA, USA

    John N. Hooker

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  2. School of Engineering and Science, Tecnologico de Monterrey, Santa Fe, Mexico

    Marzieh Khakifirooz

  3. Department of Industrial & Systems Engineering, Mississippi State University, Starkville, MS, USA

    Mahdi Fathi

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Hooker, J.N. (2019). Logic-Based Benders Decomposition for Large-Scale Optimization. In: Velásquez-Bermúdez, J., Khakifirooz, M., Fathi, M. (eds) Large Scale Optimization in Supply Chains and Smart Manufacturing. Springer Optimization and Its Applications, vol 149. Springer, Cham. https://doi.org/10.1007/978-3-030-22788-3_1

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