Mean-variance interactions in process improvement and capacity design

Abstract

We investigate mean-variance interactions of processing time as applied to process improvement and capacity design. For general capacity cost and flowcost functions, we demonstrate that production processes fall into one of six regions on the mean-variance interaction plane, each with its own policy implications. The general model is specialized to the case of an M/G/1 queue with linear and separable mean and variance costs, and with flowcosts proportional to mean queue length. Optimal solutions for processing-time mean and variance are derived, and easily obtained operating parameters are used to identify appropriate process improvement policies. A simulation example of a production network taken from industry verifies the efficacy of the linear M/G/1 model in a more general setting. We conclude that intelligent management of both processing capacity (i.e. mean processing time) and processing-time variances can be powerful tools for both capacity design and process improvement.