International Journal of Computational Science and Engineering
A comparative study of decomposition algorithms for stochastic combinatorial optimization
Computational Optimization and Applications
Computations with disjunctive cuts for two-stage stochastic mixed 0-1 integer programs
Journal of Global Optimization
A general algorithm for solving two-stage stochastic mixed 0-1 first-stage problems
Computers and Operations Research
Pre-disaster investment decisions for strengthening a highway network
Computers and Operations Research
A polynomial time algorithm for the stochastic uncapacitated lot-sizing problem with backlogging
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
A branch-and-cluster coordination scheme for selecting prison facility sites under uncertainty
Computers and Operations Research
Fenchel decomposition for stochastic mixed-integer programming
Journal of Global Optimization
Computers and Industrial Engineering
Computers and Operations Research
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Decomposition has proved to be one of the more effective tools for the solution of large-scale problems, especially those arising in stochastic programming. A decomposition method with wide applicability is Benders' decomposition, which has been applied to both stochastic programming as well as integer programming problems. However, this method of decomposition relies on convexity of the value function of linear programming subproblems. This paper is devoted to a class of problems in which the second-stage subproblem(s) may impose integer restrictions on some variables. The value function of such integer subproblem(s) is not convex, and new approaches must be designed. In this paper, we discuss alternative decomposition methods in which the second-stage integer subproblems are solved using branch-and-cut methods. One of the main advantages of our decomposition scheme is that Stochastic Mixed-Integer Programming (SMIP) problems can be solved by dividing a large problem into smaller MIP subproblems that can be solved in parallel. This paper lays the foundation for such decomposition methods for two-stage stochastic mixed-integer programs.