Please answer with proper formulas and not by a template
Sally Gordon has just completed her MBA degree and is proud to have earned a promotion to Vice President for Customer Services at the First Bank of Seattle. One of her responsibilities is to manage how tellers provide services to customers, so she is taking a hard look at this area of the bank’s operations. Customers needing teller service arrive randomly at a mean rate of 30 per hour. Customers wait in a single line and are served by the next available teller when they reach the front of the line. Each service takes a variable amount of time (assume an exponential distribution), but on average can be completed in 3 minutes. The tellers earn an average wage of $18 per hour.
A) The bank’s policy is to have no more than 10 percent chance that a customer will need to wait more
than 5 minutes before being served by a teller. How many tellers need to be used to meet this
standard? (5 marks)
B) David feels that a significant cost is incurred by making a customer wait because of potential loss
of future business. David estimates this cost to be 0.50$ for each minute the customer spends in the
bank, counting both service time and waiting time. Given this cost, how many tellers should the
bank employ? (Hint: Calculate cost of waiting as Cw * L, where L is the expected number of clients
in the system). (4 marks)
C) The bank has two types of customers: merchant customers and regular customers. The average
arrival rate for each type of customer is 15 per hour. Both types of customers currently wait in the
same line and are served by the same tellers with the same service time distribution. David is
considering changing this and the new process he is proposing will consist of two lines – one for
merchant customers and one for regular. Each line will have a single dedicated teller serving the
line. Under this configuration, what would be the average waiting time for each type of customer
before reaching a teller? (2 marks)
D) Under the dedicated server configuration in part (c), on average, how many total customers would
be in the bank, including those currently being served?