Please answer with proper formulas and not by a template Sally Gordon has just completed her MBA degree and is proud to
Posted: Sun Jul 03, 2022 1:32 pm
Please answer with proper formulas and not by a template
Sally Gordon has just completed her MBA degree and is proud tohave earned a promotion to Vice President for Customer Services atthe First Bank of Seattle. One of her responsibilities is to managehow tellers provide services to customers, so she is taking a hardlook at this area of the bank’s operations. Customers needingteller service arrive randomly at a mean rate of 30 per hour.Customers wait in a single line and are served by the nextavailable teller when they reach the front of the line. Eachservice takes a variable amount of time (assume an exponentialdistribution), but on average can be completed in 3 minutes. Thetellers earn an average wage of $18 per hour.
A) The bank’s policy is to have no more than 10 percent chance thata customer will need to wait morethan 5 minutes before being served by a teller. How many tellersneed to be used to meet thisstandard? (5 marks)B) David feels that a significant cost is incurred by making acustomer wait because of potential lossof future business. David estimates this cost to be 0.50$ for eachminute the customer spends in thebank, counting both service time and waiting time. Given this cost,how many tellers should thebank employ? (Hint: Calculate cost of waiting as Cw * L, where L isthe expected number of clientsin the system). (4 marks)C) The bank has two types of customers: merchant customers andregular customers. The averagearrival rate for each type of customer is 15 per hour. Both typesof customers currently wait in thesame line and are served by the same tellers with the same servicetime distribution. David isconsidering changing this and the new process he is proposing willconsist of two lines – one formerchant customers and one for regular. Each line will have asingle dedicated teller serving theline. Under this configuration, what would be the average waitingtime for each type of customerbefore reaching a teller? (2 marks)D) Under the dedicated server configuration in part (c), onaverage, how many total customers wouldbe in the bank, including those currently being served?
Sally Gordon has just completed her MBA degree and is proud tohave earned a promotion to Vice President for Customer Services atthe First Bank of Seattle. One of her responsibilities is to managehow tellers provide services to customers, so she is taking a hardlook at this area of the bank’s operations. Customers needingteller service arrive randomly at a mean rate of 30 per hour.Customers wait in a single line and are served by the nextavailable teller when they reach the front of the line. Eachservice takes a variable amount of time (assume an exponentialdistribution), but on average can be completed in 3 minutes. Thetellers earn an average wage of $18 per hour.
A) The bank’s policy is to have no more than 10 percent chance thata customer will need to wait morethan 5 minutes before being served by a teller. How many tellersneed to be used to meet thisstandard? (5 marks)B) David feels that a significant cost is incurred by making acustomer wait because of potential lossof future business. David estimates this cost to be 0.50$ for eachminute the customer spends in thebank, counting both service time and waiting time. Given this cost,how many tellers should thebank employ? (Hint: Calculate cost of waiting as Cw * L, where L isthe expected number of clientsin the system). (4 marks)C) The bank has two types of customers: merchant customers andregular customers. The averagearrival rate for each type of customer is 15 per hour. Both typesof customers currently wait in thesame line and are served by the same tellers with the same servicetime distribution. David isconsidering changing this and the new process he is proposing willconsist of two lines – one formerchant customers and one for regular. Each line will have asingle dedicated teller serving theline. Under this configuration, what would be the average waitingtime for each type of customerbefore reaching a teller? (2 marks)D) Under the dedicated server configuration in part (c), onaverage, how many total customers wouldbe in the bank, including those currently being served?