Computational Testing and Improvement of a Multilevel Decomposition Model for the Resource Allocation Problem
Ben Afia, Khelil
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https://hdl.handle.net/2142/70437
Description
Title
Computational Testing and Improvement of a Multilevel Decomposition Model for the Resource Allocation Problem
Author(s)
Ben Afia, Khelil
Issue Date
1981
Department of Study
Business Administration
Discipline
Business Administration
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Business Administration, General
Abstract
The research presented in this thesis deals with the study of the efficiency of a decomposition algorithm called: The Generalized Decomposition Model (GDM) as a resource allocation procedure and its improvement. There are several mathematical algorithms in the literature that deal with the problem of resource allocation, however none of them has been successfully used to solve a real problem, mainly because of inefficiencies in their analytical properties.
The GDM will be presented and its solution procedure will be illustrated via an example. By specifying the nature of some penalty functions in the objective function of the Model, two new models can be distinguished: a Linear Model and a Quadratic Model.
The most important features of the GDM are its analytical properties. It is shown that the GDM gives a feasible solution at every iteration of the interative process. It is also proven that the model converges to a limiting solution after a finite number of iterations. The nature of this limiting and the number of iterations required to reach it depends upon the version of the Model we are dealing with. The Quadratic version of the GDM is shown to converge slowly to the overall optimum solution, while the Linear Model cannot be guaranteed to do so. However, when it does converge to the overall optimum, its convergence rate is much faster than any other existing algorithms including the Quadratic Model.
Several approaches are used to study the convergence rate of the Quadratic Model. Some are found to improve significantly the convergence rate of the Model.
Finally, a new algorithm, called the Hierarchical Search Algorithm, is developed and is based on a new exchange of information procedure between the two organization's levels. The Hierarchical Search Algorithm is shown to have a much better convergence rate than the Quadratic Model.
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