Question 4 Multi-Server Queue A supermarket manager is trying to decide how many cashers to employ for the peak time. The service times for check outs are exponentially distributed with a mean service time of 3 minutes. Customer arrivals to cashiers follow a Poisson arrival process with an average 110 customers per hour. a. What is the minimum number of cashers that would be needed to have the utilization less than one? b. If the waiting time is too long, customers might leave the store or even do not enter the store. It is estimated that for every minute of waiting time, the supermarket loses a potential profit of 50 HKD every hour from lost sales. The hourly wage for a casher is 80 HKD / hour. How many cashers should the supermarket employ to maximize its profit? (Keep four decimal places.
Question 4 Multi-Server Queue
A supermarket manager is trying to decide how many cashers to employ for the peak time. The
service times for check outs are exponentially distributed with a mean service time of 3 minutes.
Customer arrivals to cashiers follow a Poisson arrival process with an average 110 customers per
hour.
a. What is the minimum number of cashers that would be needed to have the utilization less
than one?
b. If the waiting time is too long, customers might leave the store or even do not enter the
store. It is estimated that for every minute of waiting time, the supermarket loses a potential
profit of 50 HKD every hour from lost sales. The hourly wage for a casher is 80 HKD /
hour. How many cashers should the supermarket employ to maximize its profit? (Keep four
decimal places.
Step by step
Solved in 6 steps
