Optimization and extension of a production flow model

Abstract

This research is based upon a mathematical model of a production facility that was originated by A. W. Wortham. A production facility is modeled as a linear flow network of industrial processes. At each process quality control activities result in a certain proportion of processed goods being rejected or reworked. The model is used to evaluate the cost of production in relation to the interaction of quality throughput levels at the various processes. Heretofore, the primary use of a model was policy evaluation. In this research, the model is formulated as a mathematical programming problem. It is shown through a change of variables that the model gives rise to a large family of convex and concave programs that may be used to determine the optimal input and quality levels. Constant, linear, quadratic and asymptomatic functional rules relating cost and quality are used in illustrative examples. A multiproduct production system with specified demands is formulated as a concave programming problem. Penalties due to stockout and overproduction are included. A market interaction example is given that incorporates a product price dependency upon output level and marketing effort. ...