Graduate Thesis Or Dissertation
 

The maximum principle and its application to industrial engineering problems

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  • The maximum principle developed by the Russian mathematician, L.S. Pontryagin is considered to be one of the most significant contributions to the recent advances in mathematical optimization techniques. Unfortunately, most of the published literature on the application of the maximum principle is in the field of control system design, and very little has been published on the application of this principle to industrial engineering problems. The purpose of this thesis is to apply the maximum principle to practical problems in industry and business. Examples from inventory control, production planning and investment problems are presented. This thesis is also intended to critically compare the discrete version of Pontryagin's principle with other traditional optimization techniques and to present an alternate derivation of the algorithm of the discrete maximum principle. The dissertation is composed of two parts. Part I introduces briefly the basic theory of Pontryagin's maximum principle for time-optimizing continuous processes. It contains the algorithm, the derivation of the algorithm and the application to the inventory control problem. Part II discusses the discrete version of the maximum principle. It presents the statement of the algorithm, its derivation, the applications to the production planning and investment problems, and the analysis of the algorithm. Concluding remarks are presented in the last section of Part II. A tabulating programming technique based on the maximum principle has been developed for industrial and business application. Its procedure and an example are also included in Part II.
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