Case First Bank

C A S E S T U D Y

First City

National Bank

In March 1987, David Craig, vice president of operations for First City National Bank of Philadelphia was considering a change in teller operations. Currently, the bank’s tellers were arranged in pods to handle customer transactions. There were four pods containing three teller stations each. One pod was used primarily for savings accounts since some savings transactions took longer than other types of deposits or withdrawals. The major problem with the pod system was that one pod might be crowded while another was vacant. The distance between pods was such that the customers were unwilling to move from one to another.

Mr. Craig was considering two alternatives to the pod system. The first was a single-line teller arrangement as shown in Exhibit 1. Using this plan, all customers would wait in a single line until a teller became available. The person at the head of the line would then move to the open teller. Mr. Craig thought that 10 tellers would be required to handle the bank’s usual business. However, he could not be sure of the exact number without further study.

Exhibit 1 also shows the second alternative teller arrangement. Using this more conventional plan, the customers would form separate lines in front of each of the teller windows. Thus for 10 tellers, a total of 10 different lines could be formed.

In evaluating these alternatives, several issues were of utmost importance. First, Mr. Craig was concerned with both customer waiting time and teller efficiency. On the basis of past experience, Mr. Craig felt that more than 3 minutes of waiting time would be unacceptable to most customers. He also felt that teller utilization should be as high as possible, perhaps in the 80 to 90 percent range. Since demand varied during the day, the number of tellers provided would have to vary to meet the customer-service and teller-utilization goals.

Exhibit 2 - Histogram of Interarrival times

The statistical distribution of service time and arrival time is shown in Exhibits 2 and 3. The service time averages 45 seconds per customer and does not vary by time of day. On the other hand, the average time between arrivals does vary with the time of day. For example, between 11:45 and 12:45 on one particular day sampled, 431 customers arrived at the bank, with an average of 8.4 seconds between customers.

Exhibit 3 - Histogram of Service Times

To estimate the average arrival rate during different times of the day, the data in Exhibit 4 were collected. Over the period between November 1, 1986, and February 28, 1987, arrivals were counted for each half-hour period. The days were then divided into normal days, peak days, and superpeak days, depending on the intensity of the flow. Although the average number of arrivals varied during each hour of the day, the statistical pattern of arrivals was stable during each particular hour.

Normal Days Peak Days Superpeak Days

Time of Day Total

Number of Arrivals Average Arrival Rate* Total Number of Arrivals Average Arrival Rate* Total Number of Arrivals Average Arrival Rate*

8-8:30 803 19 625 22 331 25

8:30-9 919 22 758 27 418 32

9-9:30 1207 29 863 31 571 44

9:30-10 2580 63 2033 72 1228 94

10-10:30 2599 63 2237 80 1382 106

10:30-11 2870 70 2283 82 1337 103

11-11:30 3384 83 2625 94 1577 121

11:30-12 4548 111 4060 145 2325 179

12-12:30 5804 142 5329 190 2908 224

12:30-1 5351 131 4923 176 2724 210

1-1:30 4355 106 3983 142 2271 175

1:30-2 3632 89 3150 113 1991 153

2-2:30 2321 57 2012 72 1282 99

2:30-3 1935 47 1960 70 1206 93

3-3:30 2151 52 2064 74 1250 96

3:30-4 2115 52 2238 80 1328 102

4-4:30 2291 55 2340 84 1346 104

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