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A Novel Cross-decomposition Multi-cut Scheme for Two-Stage Stochastic Programming

DOI: 10.1016/b978-0-444-63456-6.50041-7
  • Cross-Decomposition
  • Stochastic Programming
  • Investment Planning
  • Computer Science
  • Mathematics


Abstract We describe a decomposition algorithm that combines Benders and scenario-based Lagrangean decomposition for two-stage stochastic programming investment planning problems with complete recourse. The first-stage variables are mixed-integer and the second-stage variables are continuous. The algorithm is based on the cross- decomposition scheme and fully integrates primal and dual information in terms of primal-dual multi-cuts added to the Benders and the Lagrangean master problems for each scenario. The benefits of the cross-decomposition scheme are demonstrated with an illustrative case study for a facility location problem with risk of disruptions.

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