Optimal Productivity and Investments in Quality: An Operations Parametric Model

Abstract In this paper we present a mathematical model of a generic manufacturing system. The quality of the manufactured product is captured through one or more of its critical design/process parameters. Managers often face the dilemma of which product/process is to be singled out for improvement in quality with the limited capital outlay on hand. In this paper, we use the critical process parameters along with the standard production variables in a mathematical programming framework, to identify the process to be targeted for improvement. Consistent high quality, results in higher rewards in a perfectly competitive market place and also requires higher amounts of the employed resources, including capital. The optimal investment to be made in achieving higher rewards depends upon the product characteristics. We consider alternative systems, which differ in their costs of quality, since the underlying process parameters follow different probability distributions. Our experiments provide some important insight into the optimal investments in quality, and the accompanying qualityproductivity trade-offs. We demonstrate that 100% process conformance or 100% use of the productive resources do not result in maximum net profits. Our model also reinforces the notion that consistent high quality ultimately translates into a corresponding gain in productivity and higher profits or net revenues.