Flexible modelling of correlated operation times with application in product-reuse facilities

Abstract

For each job (product instance) to be serviced in a product-reuse production system, multiple operations are often scheduled. Typically, there is high variability in the same operation times required by different jobs; and for each individual job, there is often significant probabilistic dependence (correlation) between many of the job's required operation times. Well-conditioned jobs require fewer operations with shorter durations. Poorly conditioned jobs require more operations with longer durations. Accurate and rapid methods for representing the uncertainty of operation necessity and duration are required to use simulation effectively as a schedule evaluation tool. This paper develops such methods using an alternative to the conventional multivariate extension of the Johnson system of univariate probability distributions. The alternative methods match the first three, and often four, marginal moments of the random vector of operation times for a given job as well as all pairwise correlations between those operation times. A logistic regression model is used to estimate the distribution of the binary random variable indicating the necessity of an operation conditioned on the indicators for the job's preceding operations. The proposed overall mixed-distribution modelling technique is computationally efficient, useful in product-reuse system practice, and easily integrated into existing simulation software platforms.

Acknowledgements

Research was supported, in part, by the Furniture Manufacturing and Management Center, North Carolina State University; the Office of Naval Research under Contract No. N00014-90-J-100; and the National Science Foundation under Grant No. DMI-9900164.