On the Numerical Solution of Stochastic Optimization Problems
نویسنده
چکیده
We introduce the stochastic linear programming (SLP) model classes, which will be considered in this paper, on the basis of a small-scale linear programming problem. The solutions for the various problem formulations are discussed in a comparative fashion. We point out the need for model and solution analysis. Subsequently, we outline the basic ideas of selected major algorithms for two classes of SLP problems: two-stage recourse problems and problems with chance constraints. Finally, we illustrate the computational behavior of two algorithms for large-scale SLP problems. keywords: stochastic linear programming, numerical methods. 1. SLP problem formulations Our starting point is a simple deterministic linear programming (LP) production problem which serves for illustrating various model formulations in stochastic linear programming (SLP). Two kinds of raw materials are used for producing a single good, and we consider a single planning period. The LPformulation for minimizing costs reads as Costs: z = 2x1 + 3x2 j m i n Capacity: zl + x2 5 100 Demand: a1 XI + a2 22 2 b (1
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