Chapter17: Project Management
Problems 1. For each of the following network diagrams, determine both the critical path and the expected project duration. The numbers on the arrows represent expected activity times. a. AOA diagram
b. AON diagram
c. AOA diagram
d. AON diagram
2. Chris received new word processing software for her birthday. She also received a check, with which she intends to purchase a new computer. Chris's college instructor assigned a paper due next week. Chris decided that she will prepare the paper on the new computer. She made a list of the activities she will need to do and their estimated times. a. Arrange the activities into two logical sequences. b. (1) Construct an AOA network diagram. (2) Construct an AON diagram. c. Determine the critical path and the expected duration time. d. What are some possible reasons for the project to take longer than the expected duration?
3. Prepare a Gantt chart for each of the following in the style of the chart shown on p. 749. a. The bank location problem (see Figure 17.4, p. 751). Hint: Use the early start (ES) times given in Table 17.3 on p. 761. b. Solved Problem number 2 on p. 776. 4. a. Develop a list of activities and their immediate predecessors similar to the lists in this problem for this diagram:
b. Construct an activity-on-arrow precedence diagram for each of the following cases. Note that each case requires the use of a dummy activity. c. Construct an AON diagram for each case.
5. For each of the problems listed, determine the following quantities for each activity: the earliest start time, latest start time, earliest finish time, latest finish time, and slack time. List the critical activities, and determine the expected duration of the project. a. Problem 1a. b. Problem 1b. c. Problem 3. 6. Reconsider the network diagram of Problem 1a. Suppose that after 12 weeks, activities 1-2, 1-3, and 2-4 have been finished; activity 2-5 is 75 percent finished; and activity 3-6 is h alf finished. How many weeks after the original start time should the project be finished? 7. Three recent college graduates have formed a partnership and have opened an adv ertising firm. Their first project consists of activities listed in the following table. a. Draw the precedence diagram. b. What is the probability that the project can be completed in 24 days or less? In 21 days or less? c. Suppose it is now the end of the seventh day and that activities A and B have been completed while activity D is 50 percent completed. Time estimates for the completion of activity D are 5, 6, and 7. Activities C and H are ready to begin. Determine the probability of finishing the project b y day 24 and the probability of finishing by day 21.
d. The partners have decided that shortening the project by two days would be beneficial, as long as it doesn't cost more than about $20,000. They have estimated the daily crashing costs for each activity in thousands, as shown in the following table. Which activities should be crashed, and what further analysis would they probably want to do?
8. The new director of special events at a large university has decided to completely revamp graduation ceremonies. Toward that end, a PERT chart of the major activities has been developed. The chart has five paths with expected completion times and variances as shown in the table. Graduation day is 16 weeks from now. Assuming the project begins now, what is the probability that the project will be completed before a. Graduation time? b. The end of week 15? c. The end of week 13?
9. What is the probability that the following project will take more than 10 weeks to complete if the activity means and standard deviations are as shown below?
10. The project described in the following table has just begun. It is scheduled to be completed in 11 weeks. a. If you were the manager of this project, would you be concerned? Explain. b. If there is a penalty of $5,000 a week for each week the project is late, what is the probability of incurring a penalty of at least $5,000?
11. The following precedence diagram reflects three time estimates for each activity. Determine: a. The expected completion time for each path and its variance. b. The probability that the project will require more than 49 weeks. c. The probability that the project can be completed in 46 weeks or less.
12. A project manager has compiled a list of major activities that will be required to install a computer information system in her firm. The list includes estimated completion times for activities and precedence relationships.
a. Construct an activity-on-node diagram for this project. b. If the project is finished within 26 weeks of its start, the project manager will receive a bonus of $1,000; and if the project is finished within 27 weeks of its start, the bonus will be $500. Find the probability of each bonus. 13. Here is a list of activity times for a project as well as c rashing costs for its activities. Determine which activities should be crashed and the total cost of crashing if the goal is to shorten the project by three weeks as cheaply as possible.
14. The project manager of a task force planning the construction of a domed stadium had hoped to be able to complete construction prior to the start of the next college football season. After reviewing construction time estimates, it now appears that a certain amount of crashing will be needed to ensure project completion before the season opener. Given the following time and cost estimates, determine a minimum-cost crashing schedule that will shave five weeks off the project length. Note: No activity can be crashed more than two weeks.
15. A construction project has indirect costs totaling $40,000 per week. Major activities in the project and their expected times are shown in this precedence diagram:
Crashing costs for each activity are
a. Determine the optimum time – cost crashing plan. b. Plot the total-cost curve that describes the least expensive crashing schedule that will reduce the project length by six weeks. 16. Chuck's Custom Boats (CCB) builds luxury yachts to customer order. CCB has landed a contract with a mysterious New York lawyer (Mr. T). Relevant data are shown on the next page. The complication is that Mr. T wants delivery in 32 weeks or he will impose a penalty of $375 for each week his yacht is late. Note: No activity can be crashed more than two weeks.
Develop a crashing schedule. 17. Given the accompanying network diagram, with times shown in days, a. Determine the expected duration of the project. b. Compute the probability that the project will take at least 18 days.
18. Create a risk matrix in the style of Figure 17.13 for this project. Use a vertical scale of $0 to $80. Which event should the project manager be most concerned about?
19. Create a risk matrix for this project:
Explain your reasoning for your placement of the events weather problems and funding delays.
