Stochastic decomposition: an algorithm for two-state linear programs with recourse
Mathematics of Operations Research
A Computational Study of Search Strategies for Mixed Integer Programming
INFORMS Journal on Computing
The Probabilistic Set-Covering Problem
Operations Research
Finding Cuts in the TSP (A preliminary report)
Finding Cuts in the TSP (A preliminary report)
Operations Research
Uncertain convex programs: randomized solutions and confidence levels
Mathematical Programming: Series A and B
Ambiguous chance constrained problems and robust optimization
Mathematical Programming: Series A and B
Convex Approximations of Chance Constrained Programs
SIAM Journal on Optimization
An Integer Programming Approach for Linear Programs with Probabilistic Constraints
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
A Sample Approximation Approach for Optimization with Probabilistic Constraints
SIAM Journal on Optimization
MIP reformulations of the probabilistic set covering problem
Mathematical Programming: Series A and B
An integer programming approach for linear programs with probabilistic constraints
Mathematical Programming: Series A and B
Operations Research Letters
The Express heuristic for probabilistically constrained integer problems
Journal of Heuristics
Improved integer programming approaches for chance-constrained stochastic programming
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Integer feasibility of random polytopes: random integer programs
Proceedings of the 5th conference on Innovations in theoretical computer science
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We present a new approach for exactly solving general chance constrained mathematical programs having discrete distributions. Such problems have been notoriously difficult to solve due to nonconvexity of the feasible region, and currently available methods are only able to find provably good solutions in certain very special cases. Our approach uses both decomposition, to enable processing subproblems corresponding to one possible outcome at a time, and integer programming techniques, to combine the results of these subproblems to yield strong valid inequalities. Computational results on a chance-constrained two-stage problem arising in call center staffing indicate the approach works significantly better than both an existing mixed-integer programming formulation and a simple decomposition approach that does not use strong valid inequalities. Thus, the strength of this approach results from the successful merger of stochastic programming decomposition techniques with integer programming techniques for finding strong valid inequalities.