Recently, there has been a growing interest in developing inventory control policies which are robust to model misspecification. One approach is to posit that nature selects a worst-case distribution for any relevant stochastic primitives from some pre-specified family. Several communities have observed that a subtle phenomena known as time inconsistency can arise in this framework. … Read more
We present in this paper a new model for robust combinatorial optimization with cost uncertainty that generalizes the classical budgeted uncertainty set. We suppose here that the budget of uncertainty is given by a function of the problem variables, yielding an uncertainty multifunction. The new model is less conservative than the classical model and approximates … Read more
We consider an uncertain variant of the knapsack problem in which the weight of the items is not exactly known in advance, but belongs to a given interval, and an upper bound is imposed on the number of items whose weight di ffers from the expected one. For this problem, we provide a dynamic programming algorithm … Read more
In this paper, we address the optimal energy storage management and sizing problem in the presence of renewable energy and dynamic pricing. We formulate the problem as a stochastic dynamic programming problem that aims to minimize the long-term average cost of conventional generation used as well as investment in storage, if any, while satisfying all … Read more
Optimization in dynamic environments is a challenging but important task since many real-world optimization problems are changing over time. Evolutionary computation and swarm intelligence are good tools to address optimization problems in dynamic environments due to their inspiration from natural self-organized systems and biological evolution, which have always been subject to changing environments. Evolutionary optimization … Read more
It is well known that most risk measures (risk functionals) are time inconsistent in the following sense: It may happen that today some loss distribution appears to be less risky than another, but looking at the conditional distribution at a later time, the opposite relation holds. In this article we demonstrate that this time inconsistency … Read more
We prove the almost-sure convergence of a class of sampling-based nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions of the decisions, and uncertainty is modelled by a scenario tree. As special cases, our results imply the almost-sure convergence of SDDP, CUPPS and DOASA when applied to … Read more
It is well known that the standard (linear) knapsack problem can be solved exactly by dynamic programming in O(nc) time, where n is the number of items and c is the capacity of the knapsack. The quadratic knapsack problem, on the other hand, is NP-hard in the strong sense, which makes it unlikely that it … Read more
In this paper we discuss time consistency of risk averse multistage stochastic programming problems. We show, in a framework of finite scenario trees, that composition of law invariant coherent risk measures can be law invariant only for the expectation or max-risk measures. CitationPreprintArticleDownload View PDF
Abstract. It is well known that multistage programs, which maximize expectation or expected utility, allow a dynamic programming formulation, and that other objectives destroy the dynamic programming character of the problem. This paper considers a risk measure at the final stage of a multistage stochastic program. Although these problems are not time consistent, it is … Read more