Graduate Thesis Or Dissertation
 

Computational improvements to Benders decomposition for generalized fixed charge problems

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  • A computationally efficient algorithm has been developed for determining exact or approximate solutions for large scale generalized fixed charge problems. This algorithm is based on a relaxation of the Benders decomposition procedure, combined with a linear mixed integer programming (MIP) algorithm specifically designed to solve the problem associated with Benders decomposition and a computationally improved generalized upper bounding (GUB) algorithm which solves a convex separable programming problem by generalized linear programming. A dynamic partitioning technique is defined and used to improve computational efficiency. All component algorithms have been theoretically and computationally integrated with the relaxed Benders algorithm for maximum efficiency for the generalized fixed charge problem. The research was directed toward the approximate solution of a particular class of large scale generalized fixed charge problems, and extensive computational results for problems of this type are given. As the size of the problem diminishes, the relaxations can be enforced, resulting in a classical Benders decomposition, but with special purpose sub-algorithms and improved convergence properties. Many of the results obtained apply to the sub-algorithms independently of the context in which they were developed. The procedure for solving the associated MIP is applicable to any linear 0/1 problem of Benders form, and the techniques developed for the linear program are applicable to any large scale generalized GUB implementation.
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