This document shows how to model two-stage stochastic linear programming problems in a GAMS environment. We will demonstrate using a small example, how GAMS can be used to formulate and solve this model as a large LP or using specialized stochastic solvers such as OSL-SE and DECIS. Finally a tailored implementation of the Benders Decomposition algorithm written in GAMS is used to solve the model.

In classical two-stage stochastic programming the expected value of the total costs is minimized. Recently, mean-risk models studied in mathematical finance for several decades have attracted attention in stochastic programming. We consider Conditional Value-at-Risk as risk measure in the framework of two-stage stochastic integer programming. The paper addresses structure, stability, and algori...

The purpose of the paper is to present existing and discuss modified optimization models and solution techniques which are suitable for engineering decision-making problems containing random elements with emphasis on two decision stages. The developed approach is called two-stage stochastic programming and the paper links motivation, applicability, theoretical remarks, transformations, input da...

background one of most important operations research problems is nurse scheduling problem (nsp) that tries to find an optimal way to assign nurses to shifts with a set of hard constraints. most of the researches are dealing with this problem in deterministic environment with constant parameters. while in the real world applications of nsp, the stochastic nature of some parameters like number of...

In this paper, a single-product, single-machine system under Markovian deterioration of machine condition and demand uncertainty is studied.  The objective is to find the optimal intervals for inspection and preventive maintenance activities in a condition-based maintenance planning with discrete monitoring framework. At first, a stochastic dynamic programming model whose state variable is the ...

Humanitarian organizations pre-position relief items in pre-disaster and distribute them to the affected areas in post-disaster. Improper planning of emergency operations causes more deaths in post-disaster. In this paper, the problem of relief item pre-positioning and multi-period distribution planning is addressed considering lateral transhipment among distribution centres to improve the effi...

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 ...

Opportunities to make sequential decisions and adjust activities as a season progresses and more information becomes available characterise the farm management process. In this paper, we present a discrete stochastic two-stage utility efficient programming model of organic dairy farms, which includes risk aversion in the decision maker’s objective function as well as both embedded risk (stochas...

mathematical modeling of supply chain operations has proven to be one of the most complex tasks in the field of operations management and operations research. despite the abundance of several modeling proposals in the literature; for vast majority of them, no effective universal application is conceived. this issue renders the proposed mathematical models inapplicable due largely to the fact th...

We consider two-stage stochastic programming problems with integer recourse. The L-shaped method of stochastic linear programming is generalized to these problems by using generalized Benders decomposition. Nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques. Finite convergence of...