Mathematical Programming

, Volume 157, Issue 1, pp 95–119 | Cite as

A cross-decomposition scheme with integrated primal–dual multi-cuts for two-stage stochastic programming investment planning problems

  • Sumit Mitra
  • Pablo Garcia-Herreros
  • Ignacio E. GrossmannEmail author
Full Length Paper Series B


We describe a cross-decomposition algorithm that combines Benders and scenario-based Lagrangean decomposition for two-stage stochastic programming investment planning problems with complete recourse, where the first-stage variables are mixed-integer and the second-stage variables are continuous. The algorithm is a novel 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 potential benefits of the cross-decomposition scheme are demonstrated with numerical experiments on a number of instances of a facility location problem under disruptions. In the original formulation, where the underlying LP relaxation is weak, the cross-decomposition method outperforms multi-cut Benders decomposition. If the formulation is improved with the addition of tightening constraints, the performance of both decomposition methods improves but cross-decomposition clearly remains the best method for large-scale problems.


Cross-decomposition Two-stage stochastic programming  Investment planning 



We would like to thank the National Science Foundation for financial support under Grant # CBET-1159443.

Supplementary material

10107_2016_1001_MOESM1_ESM.pdf (97 kb)
Supplementary material 1 (pdf 96 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2016

Authors and Affiliations

  • Sumit Mitra
    • 1
  • Pablo Garcia-Herreros
    • 1
  • Ignacio E. Grossmann
    • 1
    Email author
  1. 1.Department of Chemical EngineeringCarnegie Mellon UniversityPittsburghUSA

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