Stochastic programming problems arise in many practical situations. In general, the deterministic equivalents of these problems can be very large and may not be solvable directly by general-purpose optimization approaches. For the particular case of two-stage stochastic programs, we consider decomposition approaches akin to a regularized L-shaped method that can handle inexactness in the subpro...

Some recent developments in the area of risk aversion in stochastic integer programming are surveyed. After a discussion of modeling guidelines and resulting mean-risk stochastic integer programs emphasis is placed on structural properties of these optimization problems and on algoritms for their solution. Bibliographical notes conclude the paper.

Traditional two-stage stochastic programming is risk-neutral; that is, it considers the expectation as the preference criterion while comparing the random variables (e.g., total cost) to identify the best decisions. However, in the presence of variability risk measures should be incorporated into decision making problems in order to model its effects. In this study, we consider a risk-averse tw...

In applications of stochastic programming, optimization of the expected outcome need not be an acceptable goal. This has been the reason for recent proposals aiming at construction and optimization of more complicated nonlinear risk objectives. We will survey various approaches to risk quantification and optimization mainly in the framework of static and two-stage stochastic programs and commen...

In this paper we consider the Two-stage Stochastic Linear Programming (TSLP) problem with continuous random parameters. A common way to approximate the TSLP problem, generally intractable, is to discretize the random parameters into scenarios. Another common approximation only considers the expectation of the parameters, that is, the expected scenario. In this paper we introduce the conditional...

We formulate a risk-averse two-stage stochastic linear programming problem in which unresolved uncertainty remains after the second stage. The objective function is formulated as a composition of conditional risk measures. We analyze properties of the problem and derive necessary and sufficient optimality conditions. Next, we construct two decomposition methods for solving the problem. The firs...

Abstract Most real-world optimization problems are subject to uncertainties in parameters. In many situations where the uncertainties can be estimated to a certain degree, various stochastic programming (SP) methodologies are used to identify robust plans. Despite substantial advances in SP, it is still a challenge to solve practical SP problems, partially due to the exponentially increasing nu...

This paper discusses the practical aspects and resulting insights of the results of a two-stage mathematical network flow model to help make the decisions required to get humanitarian aid quickly to needy recipients as part of a disaster relief operation. The aim of model is to plan where to best place aid inventory in preparation for possible disasters, and to make fast decisions about how bes...