Question 1: The chief of staff in the emergency room of Exercise 6.22 is considering the computerization of the admissions process. This change will not reduce the 10 min service time, but it will make it constant. Develop a spreadsheet simulation to compare the performance of the proposed automated process with the performance of the manual existing process. Hint: Note that inter-arrival and service times that follow an exponential distribution can be generated with the Excel functions RAND() and LN() and the following expressions:
where
μ is the mean service rate
λ is the mean arrival rate
The Excel formula RAND() generates a random number between 0 and 1. The natural logarithm of the random number is found to transform this number into an exponentially distributed value. The transformation to an exponential distribution is completed when the value is divided by the appropriate mean rate and the negative sign is applied. (Simulate 500 patients in each case.)
Question 2: At Letchworth Community College, one person, the registrar, registers students for classes. Students arrive at a rate of 10/h (Poisson arrivals), and the registration process takes 5 min on the average (exponential distribution). The registrar is paid $5 per hour, and the cost of keeping students waiting is estimated to be $2 for each student for each hour waited (not including service time). Develop a process-driven spreadsheet simulation to compare the estimated hourly cost of the following three systems. (See the hint in Exercise 7.3 and simulate 500 students in each case.)
a. The current system.
b. A computerized system that results in a service time of exactly 4 min. The computer leasing cost is $7 per hour.
c. Hiring a more efficient registrar. Service time could be reduced to an average of 3 min (exponentially distributed), and the new registrar would be paid $8 per hour.