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Bender’s Decomposition Method for a Large Two-stage Linear Programming Model

Author(s): Somsakaya Thammaniwit | Peerayuth Charnsethikul

Journal: International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies
ISSN 2228-9860

Volume: 4;
Issue: 4;
Start page: 253;
Date: 2013;
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Keywords: Large-scale Stochastic Linear Programming | Feed-mix Problem Solving | MATLAB

Linear Programming method (LP) can solve many problems in operations research and can obtain optimal solutions. But, the problems with uncertainties cannot be solved so easily. These uncertainties increase the complexity scale of the problems to become a large-scale LP model. The discussion started with the mathematical models. The objective is to minimize the number of the system variables subjecting to the decision variable coefficients and their slacks and surpluses. Then, the problems are formulated in the form of a Two-stage Stochastic Linear (TSL) model incorporated with the Bender’s Decomposition method. In the final step, the matrix systems are set up to support the MATLAB programming development of the primal-dual simplex and the Bender’s decomposition method, and applied to solve the example problem with the assumed four numerical sets of the decision variable coefficients simultaneously. The simplex method (primal) failed to determine the results and it was computational time-consuming. The comparison of the ordinary primal, primal-random, and dual method, revealed advantageous of the primal-random. The results yielded by the application of Bender’s decomposition method were proven to be the optimal solutions at a high level of confidence.

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