Q5 L.L.Bean 8 points Time allocated: 20 minutes Suppose L.L.Bean has a call center which is currently staffed by only one customer service representative (CSR) who serves customers at a rate of 24 customers per hour and assume that the service time is exponentially distributed and hence the coefficient of variation for service equals 1. The customer calls come in at a rate of 20 calls/hour and has a coefficient of variation equaling 1. Assume that the inter-arrival time distribution is exponential. The process arrivals do not exhibit any systematic arrival pattern during the day and hence you can safely assume the arrivals to be stationary. The customers had been complaining about excessively long waits and the management at L.L. Bean wanted to understand the situation better and take appropriate action. Currently, the management targets the average wait (not including the process times) to not exceed 5 minutes. a) Suppose the call center uses the first-come-first-serve policy. Estimate the average wait a customer is expected to experience before their calls are answered at the call center. Are they achieving their targeted average wait times? Show calculations. Writing answers from Excel spreadsheets without explanations will be given no credit. (1.5 Marks) b) At any time, on average, how many customers will be waiting for their calls to be answered? Show calculations. (1.5 Marks) c) Suppose L.L. Bean estimates that the retailer loses $2 in sales for every minute that a customer has to wait online for a CSR, in terms of dissatisfaction with service as well as the resulting impact on future sales to disgruntled customers. If each CSR is paid $20 an hour, (1) Explain in plain English, what the tradeoffs one faces as they try to minimize the total hourly cost. (2 Marks) (ii) Give a simple equation to capture the total hourly cost. Determine the optimal number of CSRS that L.L. Bean should have to minimize the total hourly cost. Show calculations to justify your answer. (3 Marks) Q5 L.L.Bean 8 points Time allocated: 20 minutes Suppose L.L.Bean has a call center which is currently staffed by only one customer service representative (CSR) who serves customers at a rate of 24 customers per hour and assume that the service time is exponentially distributed and hence the coefficient of variation for service equals 1. The customer calls come in at a rate of 20 calls/hour and has a coefficient of variation equaling 1. Assume that the inter-arrival time distribution is exponential. The process arrivals do not exhibit any systematic arrival pattern during the day and hence you can safely assume the arrivals to be stationary. The customers had been complaining about excessively long waits and the management at L.L. Bean wanted to understand the situation better and take appropriate action. Currently, the management targets the average wait (not including the process times) to not exceed 5 minutes. a) Suppose the call center uses the first-come-first-serve policy. Estimate the average wait a customer is expected to experience before their calls are answered at the call center. Are they achieving their targeted average wait times? Show calculations. Writing answers from Excel spreadsheets without explanations will be given no credit. (1.5 Marks) b) At any time, on average, how many customers will be waiting for their calls to be answered? Show calculations. (1.5 Marks) c) Suppose L.L. Bean estimates that the retailer loses $2 in sales for every minute that a customer has to wait online for a CSR, in terms of dissatisfaction with service as well as the resulting impact on future sales to disgruntled customers. If each CSR is paid $20 an hour, (1) Explain in plain English, what the tradeoffs one faces as they try to minimize the total hourly cost. (2 Marks) (ii) Give a simple equation to capture the total hourly cost. Determine the optimal number of CSRS that L.L. Bean should have to minimize the total hourly cost. Show calculations to justify your