Chapter 9 1. Define and explain all the following terms below: a. Path: b. Activity c. Early Start d. Early Finish e. Late Start f. Late Finish g. Forward Pass h. Backward Pass i. Node j. AON k. Float

Construct the project activity network using AOA meth- odology and label each node and arrow appropriately.

Identify all dummy activities required to complete the network. Activity Duration Predecessors A 3 — B 5 A C 7 A D 3 B, C E 5 B F 4 D G 2 C H 5 E, F, G Activity Duration eS ef lS lf Slack A 3 0 3 0 3 — B 5 3 8 5 10 2 C 7 3 10 3 10 — D 3 10 13 10 13 — E 5 8 13 12 17 4 F 4 13 17 13 17 — G 2 10 12 15 17 5 H 5 17 22 17 22 — 10.5 You are considering the decision of whether or not to crash your project. After asking your operations manager to con- duct an analysis, you have determined the “precrash” and “postcrash” activity durations and costs, shown in the fol- lowing table (assume all activities are on the critical path): Normal crashed Activity Duration cost Duration cost A 4 days $1,000 3 days $2,000B 5 days 2,500 3 days 5,000 C 3 days 750 2 days 1,200 D 7 days 3,500 5 days 5,000 E 2 days 500 1 day 2,000F 5 days 2,000 4 days 3,000 G 9 days 4,500 7 days 6,300 a. Calculate the per day costs for crashing each activity.

b. Which are the most attractive candidates for crashing?

Why?

10.6 Suppose you are trying to decide whether or not it makes sense to crash your project. You know that normal project duration and direct costs are 60 days and $125,000. You are worried, though, because you have a very tight deliv- ery schedule and the customer has placed a severe pen- alty into the contract in the form of $5,000 in liquidated damages for every day the project is late after 50 days.

After working with the cost accountant, you have gener - ated the following table of project costs at different com- pletion durations: Project Duration (in days) Direct costs overhead costs Penalty charges total costs 60 $125,000 $15,500 $50,000 57 140,000 13,000 35,000 54 175,000 10,500 20,000 51 210,000 8,000 5,000 a. Complete the table. How many days would you advise the project should be crashed? Why?

b. Suppose direct costs of crashing the project only increased $5,000 per day crashed at a steady rate (start- ing with $125,000 on day 60). How many days would you advise that the project be crashed? Show your work.

10.7 When deciding on whether or not to crash project activi- ties, a project manager was faced with the following infor - mation. Activities on the critical path are highlighted with an asterisk: Normal crashed Activity cost Duration extra cost Duration A $ 5,000 4 weeks $4,000 3 weeks B* 10,000 5 weeks 3,000 4 weeks C 3,500 2 weeks 3,500 1 week D* 4,500 6 weeks 4,000 4 weeks E* 1,500 3 weeks 2,500 2 weeks F 7,500 8 weeks 5,000 7 weeks G* 3,000 7 weeks 2,500 6 weeks H 2,500 6 weeks 3,000 5 weeks a. Identify the sequencing of the activities to be crashed in the first four steps. Which of the critical activities should be crashed first? Why?

b. What is the project’s critical path? After four itera- tions involving crashing project activities, what has the critical path shrunk to? (Assume all noncritical paths are … a fully crashed critical path.) c. Suppose project overhead costs accrued at a fixed rate of $500 per week. Chart the decline in direct costs over the project life relative to the increase in overhead ex- penses.

d. Assume that a project penalty clause kicks in after 19 weeks. The penalty charged is $5,000 per week. When the penalty charges are added, what does the total proj- ect cost curve look like? Develop a table listing the costs accruing on a per-week basis.

e. If there were no penalty payments accruing to the proj- ect, would it make sense to crash any project activities?

Show your work.