We consider a version of the knapsack problem in which an item size is random and revealed only when the decision maker attempts to insert it. After every successful insertion the decision maker can choose the next item dynamically based on the remaining capacity and available items, while an unsuccessful insertion terminates the process. We … Read more
Hydropower is one of the world’s primary renewable energy sources whose usage has profound economic, environmental, and social impacts. We focus on the dispatch of generating units and the storage policy of hydro resources. In this context, an accurate assessment of the water opportunity-cost is cru- cial for driving the sustainable use of this scarce … Read more
Bellman formulated a vague principle for optimization over time, which characterizes optimal policies by stating that a decision maker should not regret previous decisions retrospectively. This paper addresses time consistency in stochastic optimization. The problem is stated in generality first. The paper discusses time consistent decision-making by addressing risk measures which are recursive, nested, dynamically … Read more
We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are uncertain, and consider quadratic decision rules for the case when only the right-hand sides are uncertain. The resulting optimization problems are NP-hard but … Read more
We consider the coordination of planning decisions of a single product in a supply chain composed of one supplier and one retailer, by using contracts. We assume that the retailer has the market power: he can impose his optimal replenishment plan to the supplier. Our aim is to minimize the supplier’s cost without increasing the … Read more
We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of n-by-n matrices and an n-dimensional vector, find a sequence of K matrices, each chosen from the given set of matrices, to maximize a convex function over the product of the K matrices and the … Read more
We consider a system with an evolving state that can be stopped at any time by a decision maker (DM), yielding a state-dependent reward. The DM does not observe the state except for a limited number of monitoring times, which he must choose, in conjunction with a suitable stopping policy, to maximize his reward. Dealing … Read more
The Stochastic Dual Dynamic Programming (SDDP) algorithm has become one of the main tools to address convex multistage stochastic optimal control problem. Recently a large amount of work has been devoted to improve the convergence speed of the algorithm through cut-selection and regularization, or to extend the field of applications to non-linear, integer or risk-averse … Read more
We consider a general class of infinite horizon dynamic programmes where state and control sets are convex and compact subsets of Euclidean spaces and (convex) costs are discounted geometrically. The aim of this work is to provide a convergence result for these problems under as few restrictions as possible. Under certain assumptions on the cost … Read more
As an alternative to traditional integer programming (IP), decision diagrams (DDs) provide a new solution technology for discrete problems based on their combinatorial structure and dynamic programming representation. While the literature mainly focuses on the competitive aspects of DDs as a stand-alone solver, we investigate their complementary role by studying IP techniques that can be … Read more