This paper considers a stochastic dynamic inventory problem involving a single item, linear cost structures, and finite distributions (but not necessarily independent) for the stochastic cost and demand parameters. We develop primal and dual algorithms for a multi-stage stochastic linear programming formulation for the problem. The complexity of the proposed algorithms is shown to be within O(N...

The capacity planning and operation problem of a multi-purpose water reservoir has been extensively studied in the literature. Optimization techniques, especially linear programming, have been used quite successfully. Although most models are robust enough as planning tools, they fall short of providing an operational policy for the shorter term. In this paper, we consider the operation of a mu...

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.

We consider the problem of bounding the expected value of a linear program (LP) containing random coe&cients, with applications to solving two-stage stochastic programs. An upper bound for minimizations is derived from a restriction of an equivalent, penalty-based formulation of the primal stochastic LP, and a lower bound is obtained from a restriction of a reformulation of the dual. Our “restr...

In this chapter, the authors propose a new approach to analyze the Solid Transportation Problem (STP). This new approach considers the multi-choice programming into the cost coefficients of objective function and stochastic programming, which is incorporated in three constraints, namely sources, destinations, and capacities constraints, followed by Cauchy’s distribution for solid transportation...

Solving a stochastic linear programming (SLP) problem involves selecting an SLP solver, transmitting the model data to the solver and retrieving and interpreting the results. After shortly introducing the SLP model classes in the first part of the paper we give a general discussion of these various facets of solving SLP problems. The second part consists of an overview on the model–solver conne...

In the present master thesis, three different algorithms, for optimizing a medium-term hydro-power planning problem with consideration of stochastic values, are presented and compared. The uncertainty arises due to varying water inflows and uncertain evolution of prices. The solution methods yield robust control strategies, which indicate for every time step, e.g. every month in one year, the o...

The amount of wheat and corn produced in excess will be sold at prices of $ 170 per ton for wheat and $ 150 per ton for corn. For sugar beets there is a quota on production which is 6000 T for the farmer. Any amount of sugar beets up to the quota can be sold at $ 36 per ton, the amount in excess of the quota is limited to $ 10 per ton. We denote by w1 and w2 the amount in tons of wheat resp. co...