In this dissertation, we investigate the problem of designing standard modules which can be used in a wide variety of products. The basic problem is: given a set of parts and products, and a list of the number of each part required in each product, how do we group parts into modules and modules into products to minimize costs and satisfy requirements. The design of computers, electronic equipments, tool kits, emergency vehicles and standard military groupings are among the potential applications for this work. Several mathematical programming models for modular design are developed and the advantages and weaknesses of each model have been analyzed. We demonstrate the difficulties, due to nonconvexity, of applying global optimization methods to solve these mathematical models. We develop necessary and sufficient conditions for satisfying requirements exactly, and use these results in several heuristic methods. Three heuristic structures; decomposition, sequential local search, and approximation, are considered. The decomposition approach extends previous work on modular design problems. Sequential local search uses a standard local solution routine (MINOS) and sequentially adds cuts on the objective function to the original model. The approximation approach uses a "least squares" relaxation to find upper and lower bounds on the objective of the optimal solution. Computational results are presented for all three approaches and suggest that the approximation approach performs better than the others (with respect to speed and solution quality). We conclude the dissertation with a stochastic variation of the modular design problem and a solution heuristic. We discuss an approximation model to the continuous formulation, which is a geometric programming model. We develop a heuristic to solve this problem using monotonicity properties of the functions. Computational results are given and compared with an upper bound.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/185431 |
| Date | January 1991 |
| Creators | Viriththamulla, Gamage Indrajith. |
| Contributors | Goldberg, Jeffrey, Sen, Suvrajeet, Tharp, Hal S. |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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