Dee F. is considering building a drive-up/drive thru coffeestall at a location she researched as a viable location. Thelocation can accommodate a maximum of 10 cars. Based on herresearch, customer arrivals follow a Poisson probabilitydistribution, with a mean arrival rate of 25 cars per hour, andthat service times follow an exponential probability distribution.Arriving customers will place their orders at an intercom stationas soon as they enter the lot where the stall will be located, andthen drive to the service window to pay for and receive theirorders. Three service alternatives are being considered:
- A single channel operation in which one employee, whose hourlywage rate is $15, fills the order and takes the money from thecustomer. The average service time for this alternative is 2minutes.
- A single-channel operation in which one employee fills theorder while a second employee takes the money from the customer.Each employee has an hourly wage of $15. The average service timefor this alternative is 1.50 minutes
- A two-channel operation with two service windows and twoemployees in each service window. Each of the employees has anhourly wage of $15. The employees stationed at each window fillsthe order and takes the money for customers arriving at the window.The average service time for this alternative is 1.5 minutes foreach channel.
- Complete the table below comparing the three alternatives onthe following service characteristics. Show your outputs used incompleting the table.
Waiting Line Effectiveness Measures | Option 1: One window, one employee | Option 2: One window, two employees | Option 3: Two windows, two employees |
Probability that there will be no car in the system. | | | |
Average number of cars waiting for service | | | |
Average time (in minutes) a car waits for service | | | |
Average time for a car to be in the system | | | |
Average number of cars in the system | | | |
The probability that an arriving car will have to wait forservice | | | |
- Which of the three options will you recommend Dee F. to use?Support your answer.