Questions:
Consider Table 6-3, Network Diagram Data for a Small Project. All duration estimates or estimated times are in days; and the network proceeds from Node 1 to Node 9.
a. Draw an AOA network diagram representing the project. Put the node numbers in circles and draw arrows from node to node, labeling each arrow with the activity letter and estimated time.
b. Identify all of the paths on the network diagram and note how long they are, using Figure 6-8 as a guide for how to represent each path.
c. What is the critical path for this project and how long is it?
d. What is the shortest possible time it will take to complete this project?
e. Review the online tutorials for Gantt and PERT charts in the third Suggested Reading by Mark Kelly in this chapter. Write a one-page paper with your answers to the questions in the tutorials. Also include any questions you had in doing the tutorials.
Answers:
a. Activity-on-Arrow (AOA) Network Diagram for a Small Project.
b. Determining the critical path for this Small Project.
Note: All duration estimates or estimated times are in days.
Path 1: A-B-E-H-K Length = 2+2+2+2+2 = 10 days
Path 2: A-C-F-H-K Length = 2+3+3+2+2 = 12 days
Path 3: A-C-F-I-J-K Length = 2+3+3+5+1+2 = 16 days
Path 4: A-D-G-J-K Length = 2+4+6+1+2 = 15 days
c. What is the critical path for this project and how long is it?
Since the critical path is the longest path through the network diagram, Path 3, A-C-F-I-J-K, length is 16 days that is critical path for this Small Project.
d. What is the shortest possible time it will take to complete this project?
Path 1, A-B-E-H-K, length is 10 days, that is the shortest possible time taken to complete this Small Project.
e. Tutorial Questions & Answers.
QUESTION 1: Which tasks are on the critical path of the PERT chart above?
Answer:
A-B-D-F-I Length is 2+3+3+3+3 = 14 days. (the longest possible path).
QUESTION 2: What is the slack time for tasks C, D and G?
Answer:
Task C: C-E Length = 1+4 = 5 days
While the top pair of task C-E is being done at the same time as the bottom pair of task D-F. Task C-E takes 1+4 = 5 days. Task D-F takes 3+3 = 6 days, so task C-E will finish one day early before task D-F finish. Therefore, either task C or task E could take one extra day to finish the project, and the slack time is one day for task C.
Task D: D-F Length = 3+3 = 6 days
Whereas task D is on the critical path, but critical tasks have no slack while they cannot run overtime without affecting the ending date of the project. Therefore, task D has no slack time accordingly.
Task G: G-H Length = 2+5 = 7 days
Task G-H takes a total of 7 days. While task B-C-E takes 3+1+4 = 8 days and task B-D-F takes 3+3+3 = 9 days. So, task G could run an extra 2 days before it caused delays, since it had to wait for task B-D-F to finish the project. Therefore, the slack time is 2 days for task G.
QUESTION 3: the person working on task C tells the project manager he can't start work until one day after the scheduled starting date. What impact would this have on the completion date of the project? Why?
Answer:
If the person cannot start work until one day after the schedule starting date, the impact would cause tasks C and E to start one day late, but would not have impact on the completion date of the project while task C-E has one day of slack to be used and the other concurrent tasks D, F joined up to begin task I.
QUESTION 4: Task A will be delayed by 2 days because some equipment has arrived late. If the project manager still wants to finish the project within the original time frame, he will need to shorten the time for one or more of the tasks. What steps can he take to reduce the number of days allocated to a task?
Answer:
If the project manager wants to finish the project within the original time frame because task A will be delayed by 2 days, then he/she could put more people to work on it, and people could work more hours in a day or company could increase the efficiency of production (e.g. automating a manual task).
QUESTION 5: The project manager decides to reduce the time needed for tasks D and F by one day each. How effective will this reduction be in achieving his aim of maintaining the original finish time for the project?
Answer:
If the project manager decides to reduce the time needed for tasks D and F by one day each, so the old critical path from 14 to 12 days. However, tasks D and F are no longer on the critical path, the new critical path A-B-C-E-I is the longest at 13 days. Therefore, the completion date of the project will be shortened by one day earlier than originally.
References
http://www.mckinnonsc.vic.edu.au/la/it/ipmnotes/ganttpert/
2. Schwalbe, K. (2006). Information technology project management (4th ed.). Boston Massachusetts: Thomson Course Technology.
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