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...

This talk discusses some modeling and solution methods for the problem of pre‐disaster transportation network protection against uncertain future disasters. Given limited resources, the goal of the central planner is to choose the best set of network components to protect while allowing the network users to follow their own best perceived routes in any resultant network configuration. This prob...

We propose a new variant of the two-stage recourse model. It can be used e.g., in managing resources in whose supply random interruptions may occur. Oil and natural gas are examples for such resources. Constraints in the resulting stochastic programming problems can be regarded as generalizations of integrated chance constraints. For the solution of such problems, we propose a new decomposition...

A new class of fuzzy stochastic optimization models—two-stage fuzzy stochastic programming with Value-at-Risk (FSP-VaR) criteria is built in this paper. Some properties of the two-stage FSP-VaR, such as value of perfect information (VPI), value of fuzzy random solution (VFRS), and bounds of the fuzzy random solution, are discussed. An Approximation Algorithm is proposed to compute the VaR by co...

In this paper, the authors solve the two stage stochastic programming with separable objective by obtaining convex polynomial approximations to the convex objective function with an arbitrary accuracy. Our proposed method will be valid for realistic applications, for example, the convex objective can be either non-differentiable or only accessible by Monte Carlo simulations. The resulting polyn...

Dynamic lot sizing problem is one of the significant problem in industrial units and it has been considered by  many researchers. Considering the quantity discount in  purchasing cost is one of the important and practical assumptions in the field of inventory control models and it has been less focused in terms of stochastic version of dynamic lot sizing problem. In  this paper, stochastic dyn...

A multistage stochastic optimization model is presented to address the scheduling of supply chains with embedded multipurpose batch chemical plants under demand uncertainty. In order to overcome the numerical difficulties associated with the resulting large-scale stochastic mixed-integer-linear-programming (MILP) problem, an approximation strategy comprising two steps, and based on the resoluti...

Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of risk. From the perspective of qualitative robustness theory, we discuss sufficient conditions for continuity of the resulting objective functions with respect ...