Solutions to Chapter 12 Exercises Chapter 12: Project Management

Chapter 12: Project Management Exercise 1 There are four paths: A-C-I (7 days) A-D-G-J (13 days) B-E-G-J (11 days) B-F-H-J (10 days) Thus, the critical path is A-D-G-J and these are the activities that should be monitored most closely because if they slip, the entire project will be delayed. Chapter 12: Project Management

Chapter 12: Project Management Exercise 1 concluded The time to complete the four paths is now: A-C-I (5.5 days) A-D-G-J (11.5 days) B-E-G-J (12.5 days) B-F-H-J (11.5 days) The critical path is now B-E-G-J and the project completion is expected to be 12.5 days. Activities G and J remain as critical activities while A and D are no longer critical. Chapter 12: Project Management

Chapter 12: Project Management Exercise 2 Chapter 12: Project Management

Chapter 12: Project Management Exercise 2: Path Slacks Path A-C-I: Slack = 6 Path A-D-G-J: Slack = 0 Path B-E-G-J: Slack = 2 Path B-F-H-J: Slack = 10 Chapter 12: Project Management

Exercise 3: Network Diagram 2 6 1 3 7 4 5 Chapter 12: Project Management

Exercise 3: Activity Expected Times, Variances and Standard Deviations Chapter 12: Project Management

Exercise 3: Path Expected Times, Variances, and Standard Deviations Chapter 12: Project Management

Exercise 3: Probability Project Finishes within 17 Weeks All paths must be considered since they all have a reasonable chance of taking longer than 17 weeks. Thus, there is a very small chance (i.e., .005%) that the project can be completed in 17 weeks or less. Chapter 12: Project Management

Exercise 3: Probability Project Finishes within 24 Weeks Only paths 1-2-6-7 and 1-3-5-7 need be considered. However, all paths can be easily included by simply changing cell B1 from 17 to 24. With all paths considered, there is a over an 86% chance of completing the project in 24 weeks. Chapter 12: Project Management

Exercise 3: Should the Project be Pursued? Using the spreadsheet it can be easily determined that the probability of finishing within 18 weeks is .176% and the probability of the project taking 22 weeks or longer is 48.321%. The expected value of the project is thus: (.176%  $10,000) + (48.321%  -$5,000) = -$2398.40 Given the negative expected value, the firm should not bid. Chapter 12: Project Management

Chapter 12: Project Management Exercise 4 The path with the longest expected time is a-b-dummy-f-h-i = 16. e 3 b 5 i 1 a 3 h 3 c 3 g 2 d 1 f 4 Chapter 12: Project Management

Chapter 12: Project Management Exercise 5 Chapter 12: Project Management

Chapter 12: Project Management Exercise 5a continued Chapter 12: Project Management

Chapter 12: Project Management Exercise 5b continued Chapter 12: Project Management

Chapter 12: Project Management Exercise 5c concluded Chapter 12: Project Management

Chapter 12: Project Management Exercise 6 # 1 # 6 # 4 # 5 # 9 # 7 # 3 # 2 # 8 Chapter 12: Project Management

Chapter 12: Project Management Exercise 6 continued Chapter 12: Project Management

Chapter 12: Project Management Exercise 6 concluded Path 2-3-4-5-7-8-9 has the longest expected time. Thus, the project would be expected to take 66.33. Chapter 12: Project Management

Chapter 12: Project Management Exercise 7 $ (000) Plan Plan Progress, % 40 30 Actual 35 24 20 17 55 70 55 70 Time, Days Time, Days Chapter 12: Project Management

Chapter 12: Project Management Exercise 7 concluded Spending variance = EC - AC = 17,000 - 30,000 = -$13,000. This indicates a cost overrun of $13,000. Schedule variance = EC - SC = 17,000 - 24,000 = -$7,000 indicating the project is behind. Time variance = TE - TA = 55 -70 = -15 days indicating a 15 day delay. Chapter 12: Project Management

Chapter 12: Project Management Exercise 8 $ (000) Plan 84 81 Value Actual 78 1 TE 2 3 Time, Months Chapter 12: Project Management

Chapter 12: Project Management Exercise 8 concluded Spending variance = EC - AC = 81,000 - 78,000 = $3,000. Schedule variance = EC - SC = 81,000 - 84,000 = -$3,000. TE can be estimated from chart by determining how much time should have elapsed according to the plan to achieve the current value completed. In this case TE is approximately 1.5 months. Thus, the spending variance = TE - TA = 1.5 - 2 = -0.5 month. Chapter 12: Project Management

Chapter 12: Project Management Exercise 9 Spending variance = EC - AC = 39,000 - 34,000 = $5,000. Schedule variance = EC - SC = 39,000 - 42,000 = -$3,000. Chapter 12: Project Management

Chapter 12: Project Management Exercise 10a Chapter 12: Project Management

Exercise 10a (concluded) Chapter 12: Project Management

Chapter 12: Project Management Exercise 10b From the above spreadsheet, the average project completion time is 90.33 days with a standard deviation of 5.16 days. Across the 100 replications of the simulation model, the project finished as quickly as 78.85 days and took as long as 103.51 days. Chapter 12: Project Management

Chapter 12: Project Management Exercise 10c Chapter 12: Project Management

Chapter 12: Project Management Exercise 10d Path A-C-F has an expected duration of 88.8 days with a standard deviation of 4.81 days. Based on this, the probability that it is completed in 80 days or less can be calculated as: From the z table in the Appendix A, the probability of the path being completed in 80 days or less is 3.51%. Alternatively, this can be found using Excel as follows: =normdist(80,88.8,4.81,true) = 3.37. Incidentally, the value found using Excel is actually more accurate since rounding the value of z was not required. Path B-D-F has an expected duration of 85.2 days and standard deviation of 7.31 days. Using Excel the probability it is completed in 80 days or less is found as: =normdist(80,85.2,7.31,true) = 23.84%. Path B-E has an expected duration of 59.0 days and standard deviation of 6.93 days. Using Excel the probability it is completed in 80 days or less is found as: =normdist(80,59,6.93,true) = 99.88%. The probability the entire project is completed in 80 days or less is calculated as (.0337)(.2384)(.9988) = 0.80% Chapter 12: Project Management

Chapter 12: Project Management Exercise 10e The results shown in the spreadsheet to part a are consistent with the probability calculated in part d. In only one of the 100 replications was the project completed in 80 days or less (i.e., rep number 14). One percent of the replications is quite close to the 0.8% calculated in part d. Chapter 12: Project Management