The principal performance measure in the Monthly Billing Time Example was the total cycle time to prepare customer bills at the end of a month.   How important is variation in systems that have a flow-time or cycle-time performance measure?  Assume we have a process that consists of a number of stations that must be performed in series.   That is, a work item must be processed by station 1 and then after completing station 1, it must be processed by station 2, and so on.    Also, assume the each station has a single server which can only process a single work item at a time.   For example, in the billing time example, a work item might be a single task the corporation performed for a customer in the previous month.  A station might determine the hours expended on that task and calculate its cost.  Assume a clerk determines the hours and calculates its cost.

Reducing the mean time for the clerk to determine the hours expended and calculate a cost will reduce the mean flow time.   What if we reduce the variation in the time a clerk takes to calculate a cost for a work item?    For illustrative purposes, assume the mean time expended by the clerk is 9 minutes to calculate the cost of a work item.  Also, assume the work item arrivals have a mean inter-arrival time of 10 minutes.

The first figure depicts the case where inter-arrival times and service times are constant, i.e., there is no variation.   The number in the system is the number of work items being served and waiting for service.  In this case no work items have to wait.   Therefore, their time at the clerk’s station is a constant 9 minutes.

The second figure illustrates the case where inter-arrival times and service times have variation.   For the five arrivals, their inter-arrival times are:  8, 7, 10, 12 and 13 minutes, for an average of 10 minutes.   Their service times are: 12, 11, 9, 7 and 6 minutes, for an average of 9 minutes.  Now the times at the work station are 12, 16, 15, 10 and 6 minutes for an average of 11.8 minutes.  The variation in inter-arrival and service times increased the time at the work station by 31%.   Thus, variation can have a significant effect on system performance when the performance measure is a flow time or cycle time.

The two figures illustrate a manual simulation for calculating the system time increase due to variation.   When analyzing an actual system, one can predict the system time using a discrete-event simulation.   Inputs to the simulation would include a flow diagram, service time distributions and system inter-arrival time distributions.   Arrival times at the individual work stations would be calculated by the simulation.