Finitely Convergent Decomposition Algorithms for Two-Stage Stochastic Pure Integer Programs

2014 ◽  
Vol 24 (4) ◽  
pp. 1933-1951 ◽  
Author(s):  
Minjiao Zhang ◽  
Si̇mge Küçükyavuz
Keyword(s):  
Decomposition Algorithms ◽  
Two Stage ◽  
Integer Programs

scholarly journals Two‐stage stochastic minimum s  −  t cut problems: Formulations, complexity and decomposition algorithms

Networks ◽  
2019 ◽  
Vol 75 (3) ◽  
pp. 235-258
Author(s):  
Steffen Rebennack ◽  
Oleg A. Prokopyev ◽  
Bismark Singh
Keyword(s):  
Decomposition Algorithms ◽  
Two Stage ◽  
Cut Problems

scholarly journals A finite branch-and-bound algorithm for two-stage stochastic integer programs

2004 ◽  
Vol 100 (2) ◽  
pp. 355-377 ◽  
Author(s):  
Shabbir Ahmed ◽  
Mohit Tawarmalani ◽  
Nikolaos V. Sahinidis
Keyword(s):  
Branch And Bound ◽  
Branch And Bound Algorithm ◽  
Two Stage ◽  
Integer Programs ◽  
Stochastic Integer Programs

Decomposition algorithms for two-stage chance-constrained programs

2014 ◽  
Vol 157 (1) ◽  
pp. 219-243 ◽  
Author(s):  
Xiao Liu ◽  
Simge Küçükyavuz ◽  
James Luedtke
Keyword(s):  
Decomposition Algorithms ◽  
Two Stage

scholarly journals Exploiting the Structure of Two-Stage Robust Optimization Models with Exponential Scenarios

2020 ◽  
Author(s):  
Hossein Hashemi Doulabi ◽  
Patrick Jaillet ◽  
Gilles Pesant ◽  
Louis-Martin Rousseau
Keyword(s):  
Robust Optimization ◽  
Single Stage ◽  
Mixed Integer ◽  
Optimization Models ◽  
Master Problem ◽  
Maximization Problem ◽  
Planning Problem ◽  
Two Stage ◽  
Integer Programs ◽  
Mixed Integer Programs

This paper addresses a class of two-stage robust optimization models with an exponential number of scenarios given implicitly. We apply Dantzig–Wolfe decomposition to exploit the structure of these models and show that the original problem reduces to a single-stage robust problem. We propose a Benders algorithm for the reformulated single-stage problem. We also develop a heuristic algorithm that dualizes the linear programming relaxation of the inner maximization problem in the reformulated model and iteratively generates cuts to shape the convex hull of the uncertainty set. We combine this heuristic with the Benders algorithm to create a more effective hybrid Benders algorithm. Because the master problem and subproblem in the Benders algorithm are mixed-integer programs, it is computationally demanding to solve them optimally at each iteration of the algorithm. Therefore, we develop novel stopping conditions for these mixed-integer programs and provide the relevant convergence proofs. Extensive computational experiments on a nurse planning problem and a two-echelon supply chain problem are performed to evaluate the efficiency of the proposed algorithms.

Tight Second Stage Formulations in Two-Stage Stochastic Mixed Integer Programs

2018 ◽  
Vol 28 (1) ◽  
pp. 788-819 ◽  
Author(s):  
Manish Bansal ◽  
Kuo-Ling Huang ◽  
Sanjay Mehrotra
Keyword(s):  
Mixed Integer ◽  
Two Stage ◽  
Integer Programs ◽  
Mixed Integer Programs ◽  
Second Stage
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