First City National Bank[1]

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 withdrawa1s. The major problem with the pod system was that one pod might he crowded while another was vacant. The distance between pods was such that 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 about 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.

The statistical distribution of service time and arrival time is shown in Exhibits 2 and 3. The service time averages 43 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.


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 and February 28, 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.

Exhibit 4: Average Customer Arrival Rates

Normal / Peak / Super Peak
Time of Day / Total Arrivals / Rate/ 30 min. / Total Arrivals / Rate/ 30 min. / Total Arrivals / Rate/ 30 min.
8:00-8:30 / 803 / 19.6 / 625 / 22.3 / 331 / 25.5
8:30-9:00 / 919 / 22.4 / 758 / 27.1 / 418 / 32.2
9:00-9:30 / 1207 / 29.4 / 863 / 30.8 / 571 / 43.9
9:30-10:00 / 2580 / 62.9 / 2033 / 72.6 / 1228 / 94.5
10:00-10:30 / 2599 / 63.4 / 2237 / 79.9 / 1382 / 106.3
10:30-11:00 / 2870 / 70.0 / 2283 / 81.5 / 1337 / 102.8
11:00-11:30 / 3384 / 82.5 / 2625 / 93.8 / 1577 / 121.3
11:30-12:00 / 4548 / 110.9 / 4060 / 145.0 / 2325 / 178.8
12:00-12:30 / 5804 / 141.6 / 5329 / 190.3 / 2908 / 223.7
12:30-1:00 / 5351 / 130.5 / 4923 / 175.8 / 2724 / 209.5
1:00-1:30 / 4355 / 106.2 / 3983 / 142.3 / 2271 / 174.7
1:30-2:00 / 3632 / 88.6 / 3150 / 112.5 / 1991 / 153.2
2:00-2:30 / 2321 / 56.6 / 2012 / 71.9 / 1282 / 98.6
2:30-3:00 / 1935 / 47.2 / 1960 / 70.0 / 1206 / 92.8
3:00-3:30 / 2151 / 52.5 / 2064 / 73.7 / 1250 / 96.2
3:30-4:00 / 2115 / 51.6 / 2238 / 79.9 / 1328 / 102.2
4:00-4:30 / 2291 / 55.9 / 2340 / 83.6 / 1346 / 103.5
4:30-5:00 / 2054 / 50.1 / 2191 / 78.3 / 1216 / 93.5
5:00-5:30 / 1598 / 39.0 / 1763 / 63.0 / 924 / 71.1

Total normal days = 41, total peak days = 28, total superpeak days = 13.

The total number of arrivals is divided by the number of days to arrive at the average arrival rate.

In order to arrive at a decision, Mr. Craig requested an analysis of the single- and multiple-line teller arrangements. For a given number of tellers, Mr. Craig wanted to know which arrangement provided the best customer service. He also specified that the analysis should include a calculation of the number of tellers required at various times of the day, so that a teller staffing plan could be devised.

In addition to the statistical analysis, Mr. Craig wondered what the customer reaction to the single-line or double-line arrangement might be. Would the appearance of a long single line drive customers away, or would the customers perceive fast service from the rapidly moving line? Mr. Craig also wondered what the other advantages and disadvantages of a single line relative to the multiple lines might be.


Discussion Questions

1.  Which alternative arrangement of teller lines should Mr. Craig select? Support your recommendation with appropriate analysis and consideration of customer reaction.

2.  For the alternative you recommend, develop appropriate staffing levels for each hour of the day.

3.  Should other alternatives, not described in the case, be considered?

B60.2350 2 Prof. Juran

[1] Source: Schroeder, R.C., Operations Management (1993) McGraw-Hill, Inc.