Question: Consider a factory that processes a single job type. Orders are processed one at a time in a serial processing configuration. One of the workstations requires a machine cleaning operation periodically. This workstation has only one machine. No more than 9 jobs can be processed between the cleaning of this machine. To insure proper cleaning of the machine, management has jobs batched at the machine in the specified group size, and then the operator cleans the machine before processing each batch. Jobs arrive at this workstation at a rate of four per hour.
An analysis of the arrival data indicates that these inter-arrival times have a squared coefficient of variation (SCV) of 1.5. The service time for individual-unit processing has a mean of 0.15 hours with an SCV of 0.75. The cleaning operation takes a mean time of one-quarter of an hour with an SCV of 1.5. Management would like to know the impact on cycle time and the departure SCV for this machine (workstation) for the various batch sizes that are feasible between 1 and 9.