Hyperrectangular partition schemes for two-stage stochastic linear mixed integer programming problems

A new exact algorithm is developed in this paper for solving two-stage stochastic linear mixed integer programming problems with pure integer variables in the first stage and continuous variables in the second stage. By combining Benders' decomposition method with hyperrectangular cut and parti...

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Bibliographic Details
Published in:Optimization Vol. 74; no. 16; pp. 4207 - 4222
Main Author: Wang, Fenlan
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 10.12.2025
Taylor & Francis LLC
Subjects:
Benders decomposition
hyperrectangular partition
Integer programming
Mixed integer
optimality gap
Optimization
Two-stage stochastic mixed integer programs
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:A new exact algorithm is developed in this paper for solving two-stage stochastic linear mixed integer programming problems with pure integer variables in the first stage and continuous variables in the second stage. By combining Benders' decomposition method with hyperrectangular cut and partition technique, we can cut off some hyperrectangulars where there is no optimal solution of the original problem. Integrating such solution scheme into a branch-and-bound framework, the proposed solution method reduces the optimality gap successively in the solution iterations. Furthermore, the proposed solution method can find the optimal solution within a finite number of iterations. The computational results show the solution method is promising.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2024.2400338