10.1 Give examples of circumstances in which a project would employ lag relationships between activities using:

a. Finish to Start

b. Finish to Finish

c. Start to Start

d. Start to Finish

10.2 The advantage of Gantt charts lies in their linkage to the project schedule baseline. Explain this concept.

10.3 What are the advantages of the use of Gantt charts over PERT diagrams? In what ways might PERT diagrams be advantageous?

10.4 How do concepts such as Brooks’s Law and the effects of sustained over time cause us to rethink the best ways to accelerate a project? Is it particularly ironic that these “acceleration” efforts can actually lead to serious delays?

10.5 Under what circumstances might you wish to crash a project?

10.6 In crashing a project, we routinely focus on those activities that lie on the critical path, not activities with slack time. Explain why this is the case.

10.7 What are some of the advantages of the use of AOA notation as opposed to AON? Under what circumstances does it seem better to apply AON methodology in network development?

10.8 Explain the concept of a dummy variable. Why is this concept employed in AOA notation? Why is there no need to use dummy variables in an AON network?

10.9 Identify and discuss some of the problems or dangers of using project networks. Under what circumstances can they be beneficial, and when can they be dangerous?

10.10 Develop a Gantt chart with the following information. What is the expected duration of the project? What is the critical path?

Activity Expected Duration Predecessors

A 12 None

B 8 None

C 5 None

D 10 A and B

E 10 C and D

F 5 A and B

10.11 Given the following information, answer the questions about this project:

Activity Expected Duration Predecessors

A 4 days —

B 9 days A

C 11 days A

D 5 days B

E 3 days B

F 7 days C

G 3 days D, F

H 2 days E, G

I 1 day H

a. Draw the network as a Gantt chart.

b. What is the critical path? Which activities have slack time?

c. What would happen if activities B and D each took 5 extra days to complete instead of the expected duration? How would the critical path change?

10.12 Develop the network activity chart and identify the critical path for a project based on the following information. Redraw the activity network as a Gantt chart. What is the expected duration of the project?

Activity Expected Duration Predecessors

A 5 days —

B 6 days A

C 2 days A

D 4 days A

E 6 days B, C

F 6 days D, E

G 12 days F

H 4 days G

I 6 days F

J 7 days H, I

10.13 Develop a Gantt chart for the following activities. Identify all paths through the network. What is the critical path? Optional: Solve this problem with Microsoft Project. How does clicking on the “Tracking Gantt” view demonstrate the critical path?

Activity Expected Duration Predecessors

A 2 days —

B 3 days A

C 4 days A

D 4 days B, C

E 5 days B

F 6 days D

G 4 days C, E, F

10.14 Reconfigure the Gantt chart in Problem 10.13 to include some different predecessor relationships. Optional: Solve this problem with Microsoft Project.

a. Assume that activities B and C are linked with a “Finish to Finish” relationship. Does that change the expected completion date for the project?

b. For activity F, add a lag of 3 days to its predecessor relationship with activity D. By adding the 3-day lag to F, what is the new expected duration for the project?

c. Suppose you now added a start-to-start relationship between activities F and G to the new Gantt chart. How does this additional relationship change the expected completion date for the project?

10.15 Consider a project with the following information. Construct the project activity network using AOA methodology 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 —

10.16 You are considering the decision of whether or not to crash your project. After asking your operations manager to conduct an analysis, you have determined the “precrash” and “postcrash” activity durations and costs, shown in the following table (assume all activities are on the critical path):

Normal Crashed

Activity Duration Cost Duration Cost

A 4 days $1,000 3 days $2,000

B 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 2,000

F 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?

10.17 Suppose you are considering crashing a project. The project’s network is as follows, along with a table identifying its critical activities and the crash costs for all tasks.

a. What is the cost of the project?

b. Which activities are the best candidates for crashing?

c. What is the expected duration of the project once it has been fully crashed?

d. What will the cost of the fully crashed project be?

B

C

D

E

F

G

Project Activities and Costs (Normal vs. Crashed)

Normal Crashed

Activity Duration

Cost

(in U.S.

dollars) Duration

Cost

(in U.S.

dollars)

A 4 days 1,000 3 days 2,000

B 6 days 1,800 3 days 3,000

C 4 days 2,500 3 days 4,000

D 9 days 2,700 6 days 6,500

E 8 days 2,400 6 days 4,500

F 5 days 3,500 3 days 7,000

G 2 days 2,400 1 day 3,000

Total costs = $16,300 $30,000

Crashing Costs

Activity Crashing Costs per Day ($) On Critical Path?

A 1,000 Yes

B 400 Yes

C 1,500 No

D 1,267 Yes

E 1,050 No

F 1,750 Yes

G 600 Yes

10.18 Suppose you are trying to decide whether or not it makes sense to crash your project. You know that the normal project duration and direct costs are 60 days and $125,000. You are worried because you have a very tight delivery schedule and the customer has placed a severe penalty 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 generated the following table of project costs at different completion

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

(starting with $125,000 on day 60). How many days would you advise that the project be crashed? Show your work.

10.19 When deciding on whether or not to crash project activities, a project manager was faced with the following information. 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

Normal Crashed

Activity Cost Duration Extra Cost Duration

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 iterations involving crashing project activities, what has the critical path shrunk too? (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 expenses.

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 project 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 project, would it make sense to crash any project activities? Show your work.