A branch-and-cut algorithm for two-stage stochastic mixed-binary programs with continuous first-stage variables

Authors:
Lewis Ntaimo;Suvrajeet Sen
Affiliations:
Department of Industrial and Systems Engineering, Texas A&M University, 3131 TAMU, College Station, TX 77843, USA.;Department of Systems and Industrial Engineering, The University of Arizona, P.O. Box 210020, Tucson, Arizona 85721, USA
Venue:
International Journal of Computational Science and Engineering
Year:
2007

Citing 11
Cited 0

Nondifferential reverse convex programs and facetial convexity cuts via a disjuntive characterization

Mathematical Programming: Series A and B
A hierarchy of relaxation between the continuous and convex hull representations

SIAM Journal on Discrete Mathematics
Continuity properties of expectation functions in stochastic integer programming

Mathematics of Operations Research
A hierarchy of relaxations and convex hull characterizations for mixed-integer zero-one programming problems

Discrete Applied Mathematics
A modification of Benders' decomposition algorithm for discrete subproblems: An approach for stochastic programs with integer recourse

Journal of Global Optimization
A finite branch-and-bound algorithm for two-stage stochastic integer programs

Mathematical Programming: Series A and B
Decomposition algorithms for stochastic combinatorial optimization: computational experiments and extensions

Decomposition algorithms for stochastic combinatorial optimization: computational experiments and extensions
The C3 Theorem and a D2 Algorithm for Large Scale Stochastic Mixed-Integer Programming: Set Convexification

Mathematical Programming: Series A and B
The Million-Variable "March" for Stochastic Combinatorial Optimization

Journal of Global Optimization
Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming

Mathematical Programming: Series A and B
On solving discrete two-stage stochastic programs having mixed-integer first- and second-stage variables

Mathematical Programming: Series A and B

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper presents a branch-and-cut method for two stage Stochastic Mixed-Integer Programming (SMIP) problems with continuous first-stage variables. This method is derived based on disjunctive decomposition (D2) for SMIP, an approach in which disjunctive programming is used to derive valid inequalities for SMIP. The novelty of the proposed method derives from branching on the first-stage continuous domain while the branch-and-bound process is guided by the disjunction variables in the second-stage. Finite convergence of the algorithm for mixed-binary second stage is established and a numerical example to illustrate the new method is given.