A Branch-and-Price Algorithm for Multistage Stochastic Integer Programming with Application to Stochastic Batch-Sizing Problems

Multistage Stochastic Unit Commitment Using Stochastic Dual Dynamic Integer Programming

Unit commitment (UC) is a key operational problem in power systems used to determine an optimal daily or weekly generation commitment schedule. Incorporating uncertainty in this already difficult mixed-integer optimization problem introduces significant computational challenges. Most existing stochastic UC models consider either a two-stage decision structure, where the commitment schedule for ...

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...

Sequential Cut Refinement Method in Multistage Stochastic Integer Programming: Application to a Unit Commitment Problem

2 Benders' method usually divides the collection of decision variables of a two-stage mathematical problem into two sets: a first set that comprises the collection of variables that represent first-stage decisions and a second set that includes the collection of variables that represent recourse actions or second-stage decisions. Usually, integer variables appear in the first set whereas the se...

A Branch-and-Bound Method for Multistage Stochastic Integer Programs with Risk Objectives

We identify multistage stochastic integer programs with risk objectives where the related wait-andsee problems enjoy similar separability as in the risk neutral case. For models belonging to this class we present a solution method combining branch-and-bound with relaxation of nonanticipativity and constraint branching along nonanticipativity subspaces.

Pairing inequalities and stochastic lot-sizing problems: A study in integer programming