Optimization models to maximize sigma quality level and Profit in a Six Sigma project

Six Sigma is at the top of the agenda for many companies that try to reduce cost and improve productivity. Companies such as Allied Signal, General Electric, Motorola, and 3M implement thousands of Six Sigma projects every year. However, Six sigma implementation requires a significant investment of capital. For example, General Electric invested about $1.6 billion between 1996 and 1999 on Six Sigma. Any investment of such high magnitude requires careful analysis to make sure that the benefit of such investment is much higher than the actual investment. Such cost benefit analysis is crucial for companies with financial constraints. In this paper, we develop two optimization models that will assist management to choose process improvement opportunities: 1. maximizing the sigma quality level of a product under cost constraints, and 2. optimal selection of processes for Six Sigma implementation to maximize returns. A hypothetical example is used to illustrate the application of the optimization models developed in the paper.