Stochastic Modeling and Control of Some Problems in Manufacturing.

Abstract

A control theoretic approach to some problems in manufacturing is examined. This approach is motivated by the recognition of the potential for enhancing system performance through the use of information feedback and on-line decision making. A class of stochastic processes, called diffusion-threshold processes, is developed. Diffusion-threshold processes are used to describe discrete event phenomena generated by underlying continuous processes. Four manufacturing problems are considered in which diffusion-threshold models are featured. The first problem considers the control of a machining process, specifically a drilling operation, with respect to economic criteria. Policies for feedrate selection and tool replacement are to be determined. The problem addresses real manufacturing issues such as uncertainty, tool failure, scrap production and the discrete nature of parts. A diffusion-threshold model for tool wear/tool life is utilized. Two types of policies are considered: age replacement policies with fixed feedrate and age based tool replacement; and feedback policies in which tool wear measurements are occasionally available and may be used to select the feedrate and make tool replacement decisions. Potential performance improvement resulting from the additional information and control freedom present in the feedback policies is investigated. Cost per time and cost per part measures are developed for the age replacement case. A class of cost functionals, called one step costs, is introduced for the feedback case. The optimal policies for both cases are described. Comparative results are presented for a special case of interest, where tool life is assumed to obey a Taylor formula in the mean. The results from the first problem are used in the development and analysis of two additional problems. The second problem considers a machine with multiple tools. The third problem considers decentralized control in serial transfer lines. The last problem uses a diffusion-threshold process to model work progress on a job. A supervisor is allowed to schedule inspections of the job and reassign resources. An optimal control formulation of the problem results in a quasi-variational inequality. The thesis offers new viewpoints of some contemporary manufacturing problems and demonstrates how new mathematical tools can be used to approach these problems.