The vast size of real world stochastic programming instances requires sampling to make them practically solvable. In this paper we extend the understanding of how sampling affects the solution quality of multistage stochastic programming problems. We present a new heuristic for determining good feasible solutions for a multistage decision problem. For power and log-utility functions we address ...

In this paper we discuss risk neutral and risk averse approaches to multistage (linear) stochastic programming problems based on the Stochastic Dual Dynamic Programming (SDDP) method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system. 2012 Elsevier B.V. All rights reserved.

A multistage stochastic optimization model is presented to address the scheduling of supply chains with embedded multipurpose batch chemical plants under demand uncertainty. In order to overcome the numerical difficulties associated with the resulting large-scale stochastic mixed-integer-linear-programming (MILP) problem, an approximation strategy comprising two steps, and based on the resoluti...

Multistage stochastic programs can be approximated by restricting policies to follow decision rules. Directly applying this idea problems with integer decisions is difficult because of the need for rules that lead integral decisions. In work, we introduce Lagrangian dual (LDDRs) multistage mixed-integer programming (MSMIP) which overcome difficulty in a MSMIP. We propose two new bounding techni...

In Shapiro [2006], estimates of the sample sizes required to solve a multistage stochastic programming problem with a given accuracy by the conditional sample average approximation method were derived. In this paper we construct an example in the multistage setting that shows that these estimates cannot be significantly improved.

Multistage stochastic programs can be seen as discrete optimal control problems with a characteristic dynamic structure induced by the scenario tree. To exploit that structure, we propose a highly eecient dynamic programming recursion for the computationally intensive task of KKT systems solution within an interior point method. Test runs on a multistage portfolio selection problem demonstrate ...

Multistage stochastic programs have applications in many areas and support policy makers in finding rational decisions that hedge against unforeseen negative events. In order to ensure computational tractability, continuous-state stochastic programs are usually discretized; and frequently, the curse of dimensionality dictates that decision stages must be aggregated. In this article we construct...

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...