A closed form formula for the waiting time would not work, since all queuing analysis assumes that a system reaches a steady state, making transient state analysis with steady state queuing formulas is inaccurate. Therefore simulation was used in the analysis of this optimization problem. We ran the simulation program in a time interval from the beginning of the day. We did this to incorporate the impact of the initial system conditions and the previous staffing decisions on the optimum number of tellers in the current time interval. Having the appropriate data as input to the simulation programs has significant impact on the accuracy of the results, like most projects the input data management was the most crucial step of the project.
Different weekdays have different workload levels.
We further classified the data and calculated the average number of transactions for each one-hour time interval, for each weekday, and for each branch by using a VB program. However just knowing the number of transactions in a time interval was not enough to determine the number of clients that get into the branch during that time interval because a customer can require more than one transaction per teller time. In the simulation program, as a customer gets into the system, the number of transactions that they require is randomly assigned according the distribution function discovered by observation. The calculations for the number of transactions input data and observations were performed for both types of clients. In order to ease the data management for the user, we developed an Excel user interface for the simulation program.