Problem 2. (10 pts)

With the information given in Problem 1, the managers of the Administrative Services Office know that students hate waiting in line before getting served. The cost of good will is $10/hour for every hour that each student waits in lines. To reduce the time a student spends waiting, they know that they need to improve Judy’s processing time (see the last problem). They are currently considering the following two options:

a.   Install a computer system, with which Judy expects to be able to complete a student request 40 percent faster (from 2 minutes per request to 1 minute and 12 seconds, for example).

b.   Hire another temporary clerk working in parallel serving a single queue, who will work at the same rate as Judy.

If the computer costs $50 to operate per day, while the temporary clerk gets paid $70 per day, is Judy right to prefer the hired help? Assume exponential interarrival times and exponential service times.

Problem 3. Customers arrive at the theater line at the rate of 100 per hour. The ticket seller averages 30 seconds per customer, which includes selling the ticket and placing validation stamps on customers ’ parking lot receipts. Assume that the interarrival times and the service times follow exponential distribution.

a.   What is the average time customers spend in the system?

b.   What would be the effect on customer time in the system of having a second ticket taker doing nothing but placing validation stamps on customers ’ parking lot receipts, thereby cutting the average service time to 20 seconds?

c.   If a second window was opened with both servers doing both tasks (sell tickets and place validation  stamps)  and  serving  a  single  queue  line,  what  is  the average customer time in the system?

Problem 4. (10 pts) You are planning a bank. You plan for six tellers. Tellers take 15 minutes per customer with a standard deviation of 8 minutes. Customers arrive one every three minutes according to an exponential distribution (recall that the standard deviation is equal to the mean). Every customer that arrives eventually gets serviced and assume that all customers stay in a single waiting line.

a.   On average, how many customers would be waiting in line?

b.   On average, how long would a customer spend in the bank?

Problem 5. (10 pts) I-mart is a discount optical shop that can fill most prescription orders in around 1 hour. The management is analyzing the processes at the store. There   currently is one person assigned to each task below. The optometrist assigned to task “B” takes an hour off for lunch and the other employees work the entire day.

For atypical 10-hour retail day (10 A.M. – 8 P.M.), the manager would like to calculate the following:

a.   What is the current maximum output of the process per day (assuming every patient requires glasses)?

b.   If one more person is available, where the shop should assign this person and what is the maximum output of the process per day?