I do not want an answer based on the excel template. please do not copy and paste your answers from online sources, I ne
Posted: Sun Jul 03, 2022 1:32 pm
I do not want an answer based on the excel template. please do not copy and paste your answers from online sources, I need to know exactly how to solve the problem
Customers at a bank 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 $18 per hour.
I need answers of part c onwards
If two tellers are used, what will be the average waiting time for a customer before getting serviceby a teller? (2 marks)b) If two tellers are used, on average how many customers will be in the bank, including thosecurrently being served? (2 marks)c) The bank’s policy is to have no more than 10 percent chance that a customer will need to wait morethan 5 minutes before being served by a teller. How many tellers need to be used to meet thisstandard? (5 marks)d) David feels that a significant cost is incurred by making a customer wait because of potential lossof future business. David estimates this cost to be 0.50$ for each minute 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 is the expected number of clientsin the system). (4 marks)e) The bank has two types of customers: merchant customers and regular customers. The averagearrival rate for each type of customer is 15 per hour. Both types of customers currently wait in thesame line and are served by the same tellers with the same service time distribution. David isconsidering changing this and the new process he is proposing will consist of two lines – one formerchant customers and one for regular. Each line will have a single dedicated teller serving theline. Under this configuration, what would be the average waiting time for each type of customerbefore reaching a teller? (2 marks)f) Under the dedicated server configuration in part (e), on average, how many total customers wouldbe in the bank, including those currently being served? How do these results compare to those frompart (b)? Is the results worse or better? (4 marks)g) David feels that if the tellers are specialized into merchant tellers and regular tellers, they would bemore efficient and could serve customers in an average of 2.5 minutes instead of 3 minutes. Answerthe questions from part (e) & (f) with this new average service time. How do the results compareto part (a) & (b)? (The goal is to compare the scenario of dedicated servers with faster service ratewith the scenario of combined servers with slower service rate.) (4 marks)
Customers at a bank 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 $18 per hour.
I need answers of part c onwards
If two tellers are used, what will be the average waiting time for a customer before getting serviceby a teller? (2 marks)b) If two tellers are used, on average how many customers will be in the bank, including thosecurrently being served? (2 marks)c) The bank’s policy is to have no more than 10 percent chance that a customer will need to wait morethan 5 minutes before being served by a teller. How many tellers need to be used to meet thisstandard? (5 marks)d) David feels that a significant cost is incurred by making a customer wait because of potential lossof future business. David estimates this cost to be 0.50$ for each minute 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 is the expected number of clientsin the system). (4 marks)e) The bank has two types of customers: merchant customers and regular customers. The averagearrival rate for each type of customer is 15 per hour. Both types of customers currently wait in thesame line and are served by the same tellers with the same service time distribution. David isconsidering changing this and the new process he is proposing will consist of two lines – one formerchant customers and one for regular. Each line will have a single dedicated teller serving theline. Under this configuration, what would be the average waiting time for each type of customerbefore reaching a teller? (2 marks)f) Under the dedicated server configuration in part (e), on average, how many total customers wouldbe in the bank, including those currently being served? How do these results compare to those frompart (b)? Is the results worse or better? (4 marks)g) David feels that if the tellers are specialized into merchant tellers and regular tellers, they would bemore efficient and could serve customers in an average of 2.5 minutes instead of 3 minutes. Answerthe questions from part (e) & (f) with this new average service time. How do the results compareto part (a) & (b)? (The goal is to compare the scenario of dedicated servers with faster service ratewith the scenario of combined servers with slower service rate.) (4 marks)