An Advanced Implementation Of The Danzig Wolfe Decomposition Algorithm For Linear Programming

Author : Andrew C. Redwood
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (115 download)

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Download or read book Dantzig-Wolfe Decomposition written by Andrew C. Redwood and published by . This book was released on 1973 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research described in this thesis is an investigation into the possibilities and implications of using Dantzig-Wolfe decomposition to solve large linear programs in a commercial computing environment. The project was carried out for the Operational Research Department of Van den Berghs and Jurgens, the Edible Oils Division of Unilever in the U.K.. The purpose of the work was to provide the Buying Department of Van den Berghs and Jurgens with a linear programming 'macro-model' capable of substantially improving their crude oil buying strategy on the international commodity market. The full multi-factory, multi-time-period model would be very large - in the region of 2500 constraints. The prohibitive cost of solving even a four-period model and the practical difficulties of maintaining the data base in a model involving so many aspects of the organisation would seem to rule out the use of such a model. The application of Dantzig-Wolfe decomposition however, a mathematical representation of decentralised planning, offers a possible solution. An algorithm for performing Dantzig-Wolfe decomposition on a single-period model of one of the factories was programmed. It was not expected that this would prove any faster than a normal simplex solution for such a small problem but the nature of the model suggested it was ideally suited for solution by decomposition techniques. Experience gained in programming this first algorithm was then made use of in the decomposition of a multi-period model of the same factory. It was previously considered that straightforward decomposition techniques were not directly applicable to linked structures such as those found in a multi-period situation, Dantzig and Wolfe themselves suggesting an elaborate multi-level decomposition in one of their original papers. In 1967, Cobb and Cord put forward an adaptation of the D-W algorithm for use with linked structures, and in this thesis, a further application of D-W theory is developed which does perform a simple single-level decomposition on multiperiod structures. Although the algorithm proved to be extremely convergent (in contrast with results obtained by previous workers in this field) the use of decomposition was not recommended to Van den Berghs for their current production requirements. A solution to the 900 row single-factory model can be achieved in about half the time required by the normal solution procedure, however the extra complexities involved in this approach outweigh the cost of computer time saved, especially when compared to the vast savings that will result from the use of multi-period models by the Buying Department. As confidence and expertise in the operation of large linear programming models increases and the implementation of a multi-factory, multi-period macro-model becomes feasible, decomposition should most certainly be used to obtain its solution.