# solution

Explain in detail A ANNO 3. (Chapter 3: 20 points). The nation of Narnia’ is near the front of the line to get millions of doses of two of the most promising COVID-19 vaccines in development that will help protect against Delta and other known variants. It is March 2021. A local pharmaceutical company has decided to develop vaccines for COVID-19 against Delta and other known variants. The company has signed a contract with the nation of Narnia to deliver millions of doses of COVID-19 vaccines. The company wants to know how long it will take to develop and release vaccines. The following table provided a slightly simplified process for vaccines development and release in Narnia. The relevant tasks involved, their immediate predecessors, and their time estimates are shown in the following table. Activity Immediate Time estimates Mean Variance Predecessor(s) (weeks) time b (t) A Identify strains None 2 4 4 0.4444 B Prepare hybridized viruses 3 7 10 6.83 1.36 C Verify hybrid viruses A 2 3 5 3.16 .25 D Distribute hybrid viruses to B 4 7 9 6.83 .69444 manufacturings E Develop testing reagents D 12 16 2016 1.777 F Setup manufacturing C 2 5 5 1 G Manufacturer vaccine E, F 2 2 2 2 0 H Test vaccine in house G 2 3 4 3 0.1111 I Vaccine packaging and release G 2 3 5 3.16 25 J Clinical test HI 2 4. 6 0.444 K Review and release vaccine (Health J 2 2 2 Canada) a) For each activity, determine expected activity times and variance. (5) b) Draw the network diagram for this project, a identify the critical path and determine the expected project duration time and variance. b. What is the expected completion time of the non-critical path(s) in the network? c. What are the variances of the non-critical paths in the network? (8) C) Suppose the operations manager of the company told the nation of Narnia the vaccines are ready in 47 weeks. a. Calculate the probability of completing cach path within 47 weeks. b. What is the probability that the vaccines will, in fact, be ready within 47 weeks? (5) d) Suppose the nation, frustrated with delayed developments, has told the general manager of the pharmaceutical company that if the vaccine is not ready within 44 weeks, it will seck alternative sources a. What is the probability that the company delivers the vaccines to the nation of Narnia with 44 weeks? (2) ??? ??? ??? | ???? 4. (Chapter 3: 10 points). Suppose you are the project manager of the pharmaceutical company in question (3). You are considering what activities you would crush if you want to finish the project in 35 weeks. ? B 6,000 D D E F 5 4 G 6,000 H Activity Activity Precedence Time in wecks Costin Dollars Descriptions relationship Normal Crash Normal Crash time (NT) time (CT) cost (NC) cost (CC) Identify strains None 4 3 8,000 11,000 Prepare hybridized A 7 5 30,000 35,000 viruses ? Verify hybrid A 3 3 6,000 viruses Distribute hybrid B 7 24,000 28,000 viruses to manufacturings Develop testing D 16 12 60,000 72,000 reagents Setup C 5,000 6,500 manufacturing Manufacturer E, F 2 2 6,000 vaccine Test vaccine in G 2 4,000 4,000 house 1 Vaccine packaging 3 2 4,000 and release Clinical test HI 4 2 4,000 6,400 K Review and release J 2 5,000 vaccine (Health Canada) For this project, the estimated indirect cost is \$2,000 per week. However, after week 40, if the vaccine is not ready, the company will pay a penalty of \$2,500 per week. For every week that the project duration is shortened – i.e., to 40 weeks – the contractor saves one week of the penalty and indirect costs, or \$2,500. For reduction beyond week 40, the savings are only the weekly indirect costs of \$4,500. a) Compute the total allowable crash time per activity and the crash cost per week for each activity. (2) b) What is the total cost required for completing the vaccine in normal time (including the penalty and indirect costs)? (2) e) Suppose that the nation of Namia needed the vaccines in 40 weeks and wanted to know how much extra cost would be incurred to develop the vaccine at this time. Crash the project to 35 weeks. Will this increase or decrease the total cost of the project? Would you crash the project to 40 weeks? Why or why not? (2) d) Would you crash the project to 35 weeks if the customer requests to do so? Why? Would you crash the project to 30 weeks? Why? (2) e) Determine the slack for activities A, B, C, E, H,&J. (2) 3 3 2 5,000 ale 5,000

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