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MS5225 Business Process Modeling & Simulation

2019-2020 Semester A

Problem 1. (30 marks)

Provide the answers to the following questions:

a) What is the 95% confidence interval?

b) Is the ``Rand()’’ function in Excel really random? What is the underlying mechanism?

c) In generating a discrete random variable, usually in Excel we construct a vlookup table and use vlookup function for Rand(). Please provide justifications for this procedure.

d) How to validate a simulation model?

e) In queueing models, if we increase the variability of arrival processes and service times, typically how the waiting time will change?

f) Why do we need to generate many samples in simulation in order to evaluate the expected objective, e.g. expected profit?

Problem 2. (30 marks)

Lilly is producing a new drug that will be sold for 10 years. Year 1 unit sales are assumed to follow will be normally distributed with mean 130,000 units and standard deviation 60,000 units. The year 0 fixed cost of developing the drug is equally likely to be $1.4 billion, $1.6 billion and $1.8 billion. Fixed cost only incurs once. Sales are equally likely to increase for 2, 3, 4, 5 years, with the average percentage increase during those years following a discrete random variable having 5% with probability 0.3, 8% with probability 0.5, and 10% with probability 0.2. During the remainder of the 10-year life of the drug, unit sales will decrease at a rate governed by a discrete random variable having 8% with probability 0.2, 12% with probability 0.5, and 18% with probability 0.3. During each year, a unit of the drug sells for $13,000. Year 1 variable cost of producing a unit of the drug is $10,000. The unit variable cost of producing the drug increases at a fixed rate 4% a year.

(a) Estimate the expected ending total profit at for the 10 years (Use the spreadsheet to simulation 500+ samples) (35 marks)

(b) Provide the sample distribution of the total profit.

(c) What is the probability that drug will generate 100 Million to Lilly?

(d) If we increase unit price the drug in Year 1 to $16,000, $17,000, $18000, $19000, respectively, what are the corresponding expected profits (using two-variable data table and 500+ samples)

Problem 3. (40 marks)

Consider an emergency room. Patients arrive to the clinic with an inter-arrival time exponential (6) minutes. Upon entering, each patient is processed by one of the two registration clerks. This takes an average of 7 minutes (exponentially distributed).  Then each patient goes to a common waiting room and waiting for one of the 5 doctors. The time that each patient spends with a doctor is (15, 20, 25) triangularly distributed. After that with probability 0.8 a patient is discharged and with probability 0.2 a patient will go for a medical test with one clerk. Each test will take exponential (10) minutes. The patient is discharged after the test.

a. Is this a terminating or non-terminating simulation? Run the simulation for 200 days with 10 days as a warm-up period. Explain the purpose of the warm-up period. Report both mean and 95% confidence interval for the cycle time (or total time) of the patients, the utilization factor of the doctors. Now set number of replications as 20 with other settings remaining the same. Report both mean and 95% confidence interval for the cycle time (or total time) of the patients, the utilization factor of the doctors. (30 marks) Save your model as q3a.doe and you just need to upload one model.

b.  If the two registration clerks have separate waiting lines, and the patient will be routed to the line with the fewest number of patients waiting in queue, ignoring whether any patient is in service. How would you change your model? (10 marks) Save your model as q3b.doe. TIPS: we can use NQ(Process 1.Queue) for the number of customer in Process 1.Queue.

c. Now suppose that for each incoming patient, with probability 0.4, one has serious conditions, and with probability 0.6 one has minor conditions. Suppose that the doctors give patients with serious conditions a higher priority. Save your model as q3c.doc (based on the model in (a) )