Management of the First Syracuse Bank is concerned about a loss of customers at its main office downtown. One solution that has been proposed is to add one or more drive-through teller stations to make it easier for customers in cars to obtain quick service without parking. Chris Carlson, the bank president, thinks the bank should only risk the cost of installing one drive-through. He is informed by his staff that the cost (amortized over a 20-year period) of building a drive-through is $12,000 per year. It also costs $16,000 per year in wages and benefits to staff each new teller window. The director of management analysis, Beth Shader, believes that the following two factors encourage the immediate construction of two drive-through stations, however. According to a recent article in Banking Research magazine, customers who wait in long lines for drive-through teller service will cost banks an average of $1 per minute in loss of goodwill. Also, adding a second drive-through will cost an additional $16,000 in staffing, but amortized construction costs can be cut to a total of $20,000 per year if two drive-throughs are installed together instead of one at a time. To complete her analysis, Shader collected one month's arrival and service rates at a competing downtown bank's drive-through stations. These data are shown as observation analyses 1 and 2 in the following tables.
(a) Simulate a 1-hour time period, from 1 to 2 P.M., for a single-teller drive-through.
(b) Simulate a 1-hour time period, from 1 to 2 P.M., for a two-teller system.
(c) Conduct a cost analysis of the two options. Assume that the bank is open 7 hours per day and200 days per year.
OBSERVATION ANALYSIS 1: INTERARRIVAL
TIMES FOR 1,000 OBSERVATIONS
TIME BETWEEN NUMBER OF
ARRIVALS (MINUTES) OCCURRENCES
1 ............... 200
2 ............... 250
3 ............... 300
4 ............... 150
5 ............... 100
OBSERVATION ANALYSIS 2: CUSTOMER
SERVICE TIME FOR 1,000 CUSTOMERS
SERVICE TIME (MINUTES) NUMBER OF OCCURRENCES
1 ............... 100
2 ............... 150
3 ............... 350
4 ............... 150
5 ............... 150
6 ............... 100