Planning horizon is a key issue in production planning. Different from previous approaches based on Markov Decision Processes, we study the planning horizon of capacity planning problems within the framework of stochastic programming. We first consider an infinite horizon stochastic capacity planning model involving a single resource, linear cost structure, and discrete distributions for genera...

The purpose of this paper is to relax the terminal conditions typically used to ensure stability in model predictive control, thereby enlarging the domain of attraction for a given prediction horizon. Using some recent results, we present novel conditions that employ, as the terminal cost, the finite-horizon cost resulting from a nonlinear controller u = −sat(Kx) and, as the terminal constraint...

Adaptive Monte Carlo methods are simulation efficiency improvement techniques designed to adaptively tune simulation estimators. Most of the work on adaptive Monte Carlo methods has been devoted to adaptively tuning importance sampling schemes. We instead focus on adaptive methods based on control variate schemes. We introduce two adaptive control variate methods, and develop their asymptotic p...

We consider stochastic nite-horizon inventory models with discrete distributions that are incompletely speciied by selected moments, percentiles, or a combination of moments and per-centiles. The objective is to determine an inventory policy that minimizes the maximum expected cost over the class of demand distributions satisfying the speciications described above. We show that many inventory m...

We present model reduction techniques to improve the efficiency and scalability of verifying probabilistic systems over a finite time horizon. We propose a finite-horizon variant of probabilistic bisimulation for discrete-time Markov chains, which preserves a bounded fragment of the temporal logic PCTL. In addition to a standard partitionrefinement based minimisation algorithm, we present on-th...

The multi-armed bandit probem is often taken as a basic model for the tradeoff between the exploration utilization required for efficient optimization under uncertainty. In this paper we study the situation in which the unknown performance of a new bandit is to be evaluated and compared with that of a known one over a finite horizon. We assume that the bandits represent random variables with di...