The Open Pit Mine Production Scheduling Problem (OPMPSP) studied in recent years is usually based on a single geological estimate of material to be excavated and processed over a number of decades. However techniques have now been developed to generate multiple stochastic geological estimates that more accurately describe the uncertain geology. While some attempts have … Read more
Progressive hedging (PH) is a scenario-based decomposition technique for solving stochastic programs. While PH has been successfully applied to a number of problems, a variety of issues arise when implementing PH in practice, especially when dealing with very difficult or large-scale mixed-integer problems. In particular, decisions must be made regarding the value of the penalty … Read more
In this paper we address a discrete capacitated facility location problem in which customers have Bernoulli demands. The problem is formulated as a two-stage stochastic program. The goal is to define an a priori solution for the location of the facilities and for the allocation of customers to the operating facilities that minimize the expected … Read more
This paper considers an important class of convex programming problems whose objective function $\Psi$ is given by the summation of a smooth and non-smooth component. Further, it is assumed that the only information available for the numerical scheme to solve these problems is the subgradient of $\Psi$ contaminated by stochastic noise. Our contribution mainly consists … Read more
We describe computational procedures to solve a wide-ranging class of stochastic programs with chance constraints where the random components of the problem are discretely distributed. Our procedures are based on a combination of Lagrangian relaxation and scenario decomposition, which we solve using a novel variant of Rockafellar and Wets’ progressive hedging algorithm. Experiments demonstrate the … Read more
The main goal of this paper is to develop accuracy estimates for stochastic programming problems by employing robust stochastic approximation (SA) type algorithms. To this end we show that while running a Robust Mirror Descent Stochastic Approximation procedure one can compute, with a small additional effort, lower and upper statistical bounds for the optimal objective … Read more
As a traditional model in the operations research and management science domain, lot-sizing problem is embedded in many application problems such as production and inventory planning and has been consistently drawing attentions from researchers. There is significant research progress on polynomial time algorithm developments for deterministic uncapacitated lot-sizing problems based on Wagner-and-Whitin property. However, in … Read more
This paper introduces disjunctive decomposition for two-stage mixed 0-1 stochastic integer programs (SIPs) with random recourse. Disjunctive decomposition allows for cutting planes based on disjunctive programming to be generated for each scenario subproblem under a temporal decomposition setting of the SIP problem. A new class of valid inequalities for mixed 0-1 SIP with random recourse … Read more
In this article, we present a representation of value-at-risk (VaR) as a difference of convex (D.C.) functions in the case where the distribution of the underlying random variable is discrete and has finitely many atoms. The D.C. representation is used to study a financial risk-return portfolio selection problem with a VaR constraint. A branch-and-bound algorithm … Read more
Outer linearization methods for two-stage stochastic linear programs with recourse, such as the L-shaped algorithm,generally apply a single optimality cut on the nonlinear objective at each major iteration, while the multicut version of the algorithm allows for several cuts to be placed at once. In general, the L-shaped algorithm tends to have more major iterations … Read more