A Study of Queuing Theory in Low to High Rework Environments with Process Availability

OF THESIS A STUDY OF QUEING THOERY IN LOW TO HIGH REWORK ENVIRONMENTS WITH PROCESS AVAILABILITY In manufacturing systems subject to machine and operator resource constraints the effects of rework can be profound. High levels of rework burden the resources unnecessarily and as the utilization of these resources increases the expected queuing time of work in process increases exponentially. Queuing models can help managers to understand and control the effects of rework, but often this tool is overlooked in part because of concerns over accuracy in complex environments and/or the need for limiting assumptions. One aim of this work is to increase understanding of system variables on the accuracy of simple queuing models. A queuing model is proposed that combines G/G/1 modeling techniques for rework with effective processing time techniques for machine availability and the accuracy of this model is tested under varying levels of rework, external arrival variability, and machine availability. Results show that the model performs best under exponential arrival patterns and can perform well even under high rework conditions. Generalizations are made with regards to the use of this tool for allocation of jobs to specific workers and/or machines based on known rework rates with the ultimate aim of queue time minimization.