In this paper we consider the adjustable robust approach to multistage optimization, for which we derive dynamic programming equations. We also discuss this from the point of view of risk averse stochastic programming.We consider as an example a robust formulation of the classical inventorymodel and show that, like for the risk neutral case, a basestock policy is optimal. © 2011 Elsevier B.V. A...

In this paper we derive estimates of the sample sizes required to solve a multistage stochastic programming problem with a given accuracy by the (conditional sampling) sample average approximation method. The presented analysis is self contained and is based on a, relatively elementary, one dimensional Cramér’s Large Deviations Theorem.

Multi-homing is a technology used by Internet Service Provider (ISP) to connect to the Internet via different network providers. To make full use of the underlying networks with minimum cost, an optimal routing strategy is required by ISPs. This study investigates the optimal routing strategy in case where network providers charge ISPs according to top-percentile pricing. We call this problem t...

In this chapter, we present the multistage stochastic programming framework for sequential decision making under uncertainty and stress its differences with Markov Decision Processes. We describe the main approximation technique used for solving problems formulated in the multistage stochastic programming framework, which is based on a discretization of the disturbance space. We explain that on...

The paper presents a new algorithmic approach for multistage stochastic programs which are 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 a primal-dual interior point method. Co...

We study multistage tracking error problems. Different tracking error measures, commonly used in static models, are discussed as well as some problems which arise when we move from static to dynamic models. We are interested in dynamically replicating a benchmark using only a small subset of assets, considering transaction costs due to rebalancing and introducing a liquidity component in the po...

Handling uncertainty in natural inflow is an important part of a hydroelectric scheduling model. In a stochastic programming formulation, natural inflow may be modeled as a random vector with known distribution, but the size of the resulting mathematical program can be formidable. Decomposition-based algorithms take advantage of special structure and provide an attractive approach to such probl...

Airlines must dynamically choose how to allocate their flight capacity to incoming travel demand. Because some passengers take connecting flights, the decisions for all network flights must be made simultaneously. To simplify the decision making process, most practitioners assume demand is deterministic and equal to average demand. We propose a multistage stochastic programming approach that mo...

It is well known that risk-averse multistage stochastic optimization problems are often not in the form of a dynamic stochastic program, i.e. are not dynamically decomposable. In this paper we demonstrate how some of these problems may be extended in such a way that they are accessible to dynamic algorithms. The key technique is a new recursive formulation for the Average Value-atRisk. To this ...

Multistage stochastic programs show time-inconsistency in general, if the objective is neither the expectation nor the maximum functional. This paper considers distortion risk measures (in particular the Average Value-at-Risk) at the final stage of a multistage stochastic program. Such problems are not time consistent. However, it is shown that by considering risk parameters at random level and...