On a Class of Multistage Stochastic Hierarchical Problems

Hierarchical Sparsity in Multistage Convex Stochastic Programs

Statistical inference of multistage stochastic programming problems

We discuss in this paper statistical inference of sample average approximations of multistage stochastic programming problems. We show that any random sampling scheme provides a valid statistical lower bound for the optimal value of the true problem. However, in order for such lower bound to be consistent one needs to employ the conditional sampling procedure. We also indicate that fixing a fea...

Solving Multistage Mixed Nonlinear Convex Stochastic Problems

We present an algorithm to solve multistage stochastic convex problems, whose objective function and constraints are nonlinear. It is based on the twin-node-family concept involved in the Branch-and-Fix Coordination method. These problems have 0–1 mixed-integer and continuous variables in all the stages. The non-anticipativity constraints are satisfied bymeans of the twin-nodefamily strategy. I...

A special Class of Stochastic PERT Networks

Considering the network structure is one of the new approaches in studying stochastic PERT networks (SPN). In this paper, planar networks are studied as a special class of networks. Two structural reducible mechanisms titled arc contraction and deletion are developed to convert any planar network to a series-parallel network structure.&#10In series-parallel SPN, the completion time distribution...

On solving strong multistage nonsymmetric stochastic mixed 0-1 problems

In this note we present the basic ideas of a parallelizable Branch-andFix Coordination algorithm for solving medium and large-scale multistage mixed 0-1 optimization problems under uncertainty, where this one is represented by nonsymmetric scenario trees. An assignment of the constraint matrix blocks into independent scenario cluster MIP submodels is performed by a named cluster splitting varia...