**Project management model; Model building and decision analysis; Monte Carlo Simulation**

**Assignment 4**

(1) Read chapter 9. Answer review questions

1.1. 6

1.2. 7

Read chapter 10 (until it starts talking about crystal ball software). Answer review question

1.3. 1

1.4. Answer the following question – Is Risk from PDF or CDF? What question do you ask CDF to estimate risk?

(2)Project management model

2.1. Chapter 9 –Solve problem 18. Also include the graphical representation.

2.2. Solve the problem again to calculate critical path assuming task W takes 7 units of time to complete.

(3)Model building and decision analysis

3.1. Chapter 9 – Solve problem 15.

3.2. Solve the problem again if KVA can handle 138 patients per week.

(4) Monte Carlo Simulation

Outsourcing decision model (see slides for model setup and procedure), input parameters:

- Cost to manufacture is weibull distributed between 90 and 160. Use data in assignment 2.
*If you are not confident about your Weibull distribution, assume data is normally distributed between 90 and 160. Mean = (90+160)/2. STD = select a value between 10-15.*__You will not lose any points for this.__ - Cost to outsource is normally distributed with mean 172 and STD of 13.
- Capital is one of {50010, 52500, 47300, 51600, 48440}
- Demand is uniformly distributed between 830 to 999

4.1. Determine probability of decision variable = Outsourcing. Hint: see slides 35 to 37.

4.2. What is the probability that manufacturing cost is less than 90% of its maximum value in your model?

4.3. What is the probability that outsourcing cost is less than 85% of its maximum value in its model?

4.4. Add 95% confidence limits on probability of decision variable = Outsourcing from 4.1 (Hint: see week 2 slides. Confidence interval for fraction)

Note that this is from empirical data (monte carlo simulation) and not a theoretical model.

(5)PDF and CDF calculation on monte carlo simulation using regression

5.1. Using your knowledge of regression fit the PDF of cost differencein problem above to a mathematical model. Hint: see slides 38 to 43.

5.2. Calculate RMS error and Chi Sq. fit between PDF from empirical data (previous problem PDF) and your regression model (current problem PDF).

5.3. From the PDF calculate CDF.

5.4. Verify answers for problems 4.1 using CDF calculated from regression model. Are they close?

Important Note: Save your work. We will revisit this problem.