Lagrangian solution techniques and bounds for loosely coupled mixed-integer stochsatic programs

Many production problems involve facility setups that lead to integer variables, production decisions that are continuous, and demands that are likely to be random. While these problems can be quite difficult to solve, a model and an efficient solution technique are proposed for this basic class of...

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Bibliographic Details
Published in:Operations research 2000-01, Vol.48 (1), p.91
Main Authors: Takriti, Samer, Birge, John R
Format: Article
Language:English
Subjects:
Integer programming
Mathematical models
Optimization
Production scheduling
Stochastic models
Studies
Online Access:Get full text
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Summary:Many production problems involve facility setups that lead to integer variables, production decisions that are continuous, and demands that are likely to be random. While these problems can be quite difficult to solve, a model and an efficient solution technique are proposed for this basic class of stochastic mixed-integer programs. A set of scenarios are used to reflect uncertainty. The resulting mathematical model is solved using Lagrangian relaxation. It is shown that the duality gap of the relaxation is bounded above by a constant that depends on the cost function and the number of branching points in the scenario tree. The technique is applied to the problem of generating electric power. Numerical results indicate significant savings when the stochastic model is used instead of a deterministic one.
ISSN:0030-364X
1526-5463