MIME 4100 Final Exam 4/25/2007

Due Thursday, 5/3/2007, 5:00 PM. Please put your solution in a large envelop with your name on it and bring it to my office (NI 4035) in person between 3:00 PM to 5:00 PM on Thursday, 5/3/2007. No solutions will be accepted before 3:00 PM or after 5:00 PM.

This is a take-home exam. Open book, no time limit. Please sign the honor pledge: I have not given or received any help in this exam. Name ______, Signature ______

For the two problems below submit hardcopies of the following:

a)  A write-up explaining the logic for developing your model and the steps that you followed to develop this model.

b)  A printout showing your Arena model.

c)  The report from Arena. Export the report in a PDF or word file and print it.

d)  A write-up explaining your observations are conclusions.

1.  (50 pts) Study the example of the simple call center system in sections 5.1 to 5.4 of the text. Consider the following changes in the system. After a sales call has been accepted to the system and directed to the sales queue, an automated message tells the caller what the caller’s order is in the queue. A caller stays in the queue only if one or no callers are ahead of him/her. Otherwise the customer leaves without taking to a salesperson and does not return. This action is called balking. Modify the Arena model for this example to account for customer balking and to count the number of prospective customers who leave the system without talking to a salesperson.

Run your model for 10 hours using the same terminating conditions as for the example in section 5.1 of the text. Study the Arena report, and compare the results with those from the original model. Examine if it is important to account for customer balking in the model. Summarize the observations and conclusions of the study.

2.  (50 pts) A gas station has two pumps. Cars arrive at the station with interarrival time that is exponentially distributed with a mean value of 2.5 minutes. If a car arrives and both pumps are busy then it leaves the station without waiting for service and does not return. The number of gallons of gas sold per car, GAL, follows a discrete probability distribution shown in the table below:

Gallons (GAL) / Probability
7 / 0.05
8 / 0.1
9 / 0.2
10 / 0.3
11 / 0.2
12 / 0.1
13 / 0.05

The time required to pump the gas per car is PT (minutes) where:

PT=0.2*GAL+PAYTIM

and PAYTIM is the time required to pay. PAYTIM is a random variable, which is independent of GAL and follows the Weibull distribution with scale parameter of 0.8, and shape parameter of 0.5. The station makes a profit of $0.08 per gallon sold. Build an Arena model to simulate the operation of the pump and estimate the daily profit. Assume that the station opens at 8 AM and closes at 6 PM and simulate the operation of the gas station for one day. Create an animated plot of the cumulative profit as a function of time.

Study the Arena report, and compare the results with those from the original model. Summarize the conclusions of the study.