# Mathematical programming models and heuristics for standard modular design problem.

http://hdl.handle.net/10150/185431
Title:
Mathematical programming models and heuristics for standard modular design problem.
Author:
Viriththamulla, Gamage Indrajith.
Issue Date:
1991
Publisher:
The University of Arizona.
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.
Abstract:
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.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Dissertations, Academic; Modularity (Engineering); Industrial engineering.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Systems and Industrial Engineering; Graduate College
Degree Grantor:
University of Arizona
Goldberg, Jeffrey

DC FieldValue Language
dc.language.isoenen_US
dc.titleMathematical programming models and heuristics for standard modular design problem.en_US
dc.creatorViriththamulla, Gamage Indrajith.en_US
dc.contributor.authorViriththamulla, Gamage Indrajith.en_US
dc.date.issued1991en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © 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.en_US
dc.description.abstractIn 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.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectModularity (Engineering)en_US
dc.subjectIndustrial engineering.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineSystems and Industrial Engineeringen_US
thesis.degree.grantorUniversity of Arizonaen_US