# Waiting Line Case: Polonius National Bank

1429 words - 6 pages

The Case.The goal of this case study was to gain a further understanding and application skills of waiting line analysis. This case analyzed the existing staffing policies for Polonius National Bank (PNB). The goal of the analysis was to determine the optimal number of cashiers that the bank should staff using a waiting line model. Once this optimal number of cashiers was decided upon, it was necessary to determine for what range of goodwill costs the number of cashiers would remain the same.Data.The data was gathered at a particular time when the arrival rates and service time patterns were expected to be consistent on a day to day basis. It was determined that this time was from 9:00 A.M. ...view middle of the document...

This was calculated in a similar fashion as the expected number of arrivals per minute. The probability was calculated by dividing the number of observations for each time interval by the total number of observations. The time intervals 25 second intervals ranging from 0 to 2.5 minutes. Then the product was calculated by multiplying the midpoint time by the probability. The product was summed to give an expected service time of .33 minutes per customer. Translated to minutes the average service rate per channel (μ) was 3 customers per minute. Thus the expected arrival rate and service rate were calculated, allowing for proper analysis of the data.Model selection.Depending on the flow of customers to be serviced (from our infinite customer population), we need to decide on the optimal number of tellers. Since more than 5 customers are arriving per minute, while a teller is able to serve only 3 customers per minute, we reject the single channel models 1 and 2. Model 2 is also rejected because in figure 2 we find that our service pattern is not constant.The waiting line model used in analyzing the data was Model 3, characterized by: multiple channels, infinite source population, Poisson arrival pattern, and exponential service rate. It was assumed that the data matches closely enough to the Poisson and Exponential probabilities for arrival rate of 5.498 and service rate of 3. This comparison is shown in Figures 1 and 2.Figure 1Figure 2Analysis.In order to determine the optimal number of channels, the total cost had to be determined for each number of staffed channels. For channel numbers higher than 1 the following process was used to determine the total cost. The first step was to determine the number of customers in line (nl). This was found using the tables for infinite source population, based on the number of channels. This table is only useful for up to 5 channels. The second step was to calculate total number of customers in the system at any given time (ns) for each number of channels used. This was calculated by adding (nl) to (λ/ μ). From there the total cost of each staffing option was found by calculating the cost of the cashiers per hour (\$25 multiplied by the number of tellers) then adding the goodwill cost (multiplying the number of customers in the system by \$175). Table 1 shows the calculations for a goodwill cost of...

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