First City National Bank1 Sandra Boxer, vice president of operations for First City National Bank of Philadelphia is considering a change in teller operations. Currently, the bank's tellers are arranged in pods to handle customer transactions. There are four pods containing three teller stations each. One pod is used primarily for savings accounts since some savings transactions take longer than other types of deposits or withdrawals. The major problem with the pod system is that one pod might be crowded while another is vacant. The distance between pods is such that the customers are unwilling to move from one to another. Ms. Boxer is considering two alternatives to the pod system. The first is 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. Ms. Boxer thinks that 10 tellers would be required to handle the bank's usual business. However, she can not be sure of the exact number without further study. Exhibit 1. Teller Arrangements 1 This case study was adapted and modified for teaching purposes from Schroeder, R.G. (1993). Operations Management. McGraw Hill. 1 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 are of utmost importance. First, Ms. Boxer is concerned with both customer waiting time and teller efficiency. On the basis of past experience, Ms. Boxer feels that more than 3 minutes of waiting time is unacceptable to most customers. She also feels that teller utilization should be as high as possible, perhaps in the 80 to 90 percent range. Since demand varies during the day, the number of tellers provided needs to vary to meet the customer-service and teller-utilization goals. Exhibit 2. Histogram of Interarrival times 2 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 1st and February 28th, 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 3 number of arrivals varied during each hour of the day, the statistical pattern of arrivals was stable during each particular hour. Normal Days Time of Day 8-8:30 8:30-9 9-9:30 9:30-10 10-10:30 10:30-11 11-11:30 11:30-12 12-12:30 12:30-1 1-1:30 1:30-2 2-2:30 2:30-3 3-3:30 3:30-4 4-4:30 4:30-5 5-5:30 Total Number of Arrivals 803 919 1207 2580 2599 2870 3384 4548 5804 5351 4355 3632 2321 1935 2151 2115 2291 2054 1598 Average Arrival Rate* 19 22 29 63 63 70 83 111 142 131 106 89 57 47 52 52 55 50 39 Peak Days Total Number of Arrivals 625 758 863 2033 2237 2283 2625 4060 5329 4923 3983 3150 2012 1960 2064 2238 2340 2191 1763 Average Arrival Rate* 22 27 31 72 80 82 94 145 190 176 142 113 72 70 74 80 84 78 63 Superpeak Days Total Number of Arrivals 331 418 571 1228 1382 1337 1577 2325 2908 2724 2271 1991 1282 1206 1250 1328 1346 1216 924 Average Arrival Rate* 25 32 44 94 106 103 121 179 224 210 175 153 99 93 96 102 104 93 71 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. Exhibit 4. Chart Of Average Customer Arrival Rates In order to arrive at a decision, Ms. Boxer requested an analysis of the single- and multiple-line teller arrangements. For a given number of tellers, Ms. Boxer wanted to know which arrangement provided the best customer service. She 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, Ms. Boxer 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? Ms. Boxer also wondered what the other advantages and disadvantages of the single line relative to the multiple lines might be. 4 DISCUSSION QUESTIONS 1. Which alternative arrangement of teller lines should Ms. Boxer 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? 5