# Supply Chain

## Conceptual Questions (10 points each)

C1. Explain the concept “slack” in project management? What’s the connection – and what’s the difference –between slack on a single activity and slack on a path?

C2. What assumptions are needed to calculate the probability that a project will be completed by a target date? When might these assumptions not be well satisfied?

C3. Is the critical path necessarily the path that poses the greatest risk for a project manager?

C4. Using Internet resources, identify a large firm that offers project management services. Explain briefly one of their recent project management contracts.

## Quantitative Questions (20 points each)

1. The following table describes a project prior to any crashing of activities. For every week that the project duration extends beyond 25 weeks, there is a penalty of \$1,000. Indirect costs on this project are \$2,500 per week.

 Activity Predecessor(s) NT (weeks) CT (weeks) NC (\$000) CC (\$000) A None 5 3 2 4 B None 9 8 4 7 C A 10 8 10 12 D A, B 4 3 3 7 E B 3 2 4 5 F D 9 6 4 10 G E, F 2 2 2 2 H G 9 6 8 11 I C, F 9 7 7 15

(a) What path(s) is/are critical, prior to any crashing of activities?

(b) What is the duration of the project prior to any crashing of activities?

(c) After appropriate crashing of activities, what is the duration of the minimum cost project? (d) What path(s) is/are critical in the minimum cost project?

(e) How much cheaper is the minimum cost project, compared to the project before crashing?

2. The following table describes a project.

 Activity Predecessor(s) Time (days) A None 7 B None 5 C B 3 D A 2 E A, B 5 F D, E 9 G C, E 3

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POM 610 632, Fall 2019. Assignment #2.

(a) You need to ensure that the project is completed as soon as possible. The activities cannot however be crashed. You have one other option: you could reassign one employee, who is currently scheduled to work on Activity G, to help the employee scheduled to work on Activity F. Each day that you reassign the employee will entail that Activity G increases its time by one day, but and Activity F reduces its time by one day. How many days should you reassign the employee?

(b) Draw a Gantt chart for this project, using EF-EF for the critical activities, the ES-EF time for noncritical activities, and the slack time for non-critical activities.

3. The following table describes a project.

 Activity Predecessor(s) a (days) m (days) b (days) A None 20 30 40 B A 80 84 100 C A 46 60 98 D C 30 50 76 E B 25 30 41 F D, E 25 30 35 G F 10 20 30 H G 20 25 60 I G 8 10 12 J H, I 20 25 60

(a) What path(s) is/are critical? What is the expected project duration?

(b) Considering the critical path, what is the probability of completing the project in 265 days?

(c) For the second-longest path, what is the probability of completion in 265 days?

(d) If the project manager wants to set a project deadline such that there is 90% chance of completing the project by the deadline, how many days is the deadline?