A 1 Problem 12 B C D E F G H K L M N 2 3 Given: 4 Given: 5 6 We are given the following times (optimistic, most likely, and pessimistic) for each activity in the table below. Most 7 Activity Optimistic Likely Pessimistic Mean Variance 8 A 2 4 6 4 16/36 9 D 6 8 10 8 16/36 10 E 7 9 12 9.17 25/36 11 H 2 3 5 3.17 936 12 F 3 4 8 4.5 25/36 13 G 5 7 9 7 16/36 14 B 2 2 3 2.17 136 15 I 2 3 6 3.33 16/36 16 J 3 4 5 4 4 36 17 K 4 5 8 5.33 16/36 18 C 5 8 12 8.17 49/36 19 M 1 1 1 1 0/36 20 N 6 7 11 7.5 25/36 21 8 9 13 9.5 25/36 22 End 23 24 25 a. construct a network diagram 26 27 b. Project manager will receive a bonus of $1,000 if the project is finished within 26 weeks Path T26: 28 There are 4 paths so repeat for each path (use you network diagram) 29 Path A-D-E-H 30 Expected completion time=4+8+9.17+3.17=24.34 31 Variance=16/36 +16/36 +25/36+9/36 =66/36 32 Standard deviation v66/36 = 1.354 33 z 26-24.34/1.354 = 1.23 34 Using Appendix B: Probability of completion 26 weeks = 0.8907 35 Table B.2 JJ A B C D E F G H J K L M N 36 Path 2 37 38 39 40 41 42 43 Path 3 44 45 46 47 48 49 50 Path 4 51 52 53 54 55 56 57 Conclusion Probability of receiving a bonus of $1,000 = Probability (0.8907 XPath 2 X Path 3 X Path 4)= 58 59 60 b-2. Project manager will receive a bonus of $500 if the project is finished within 27 weeks Path T27: 61 There are 4 paths so repeat for each path (use you network diagram) 62 Path A-D-E-H 63 Expected completion time=4+8+9.17+3.17=24.34 64 Variance=16/36 +16/36 +25/36+9/36=66/36 65 Standard deviation V66/36 = 1.354 66 z=27-24.34/1.354 = 1.96 Remember if the z value > +3.00 treat the prbability of completion as being = 1.0000 67 Using Appendix B: Probability of completion $27 weeks = 0.9750 68 69 Path 2 70 71 A B C D E 72 73 74 75 76 Path 3 77 78 79 80 81 82 83 Path 4 84 85 86 87 88 89 FL G H K L M N 90 Conclusion Probability of receiving a bonus of $1,000-Probability (0.9750 X Path 2 X Path 3 X Path 4)= 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 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. Immediate Estimated Activity Predecessor Times (weeks) A 2-4-6 D A 6-8-10 E 7-9-12 H H E 2-3-5 F A 3-4-8 G F 5-7-9 Immediate Estimated Activity Predecessor Times (weeks) B 2-2-3 I B 2-3-6 J I 3-4-5 K J 4-5-8 C 5-8-12 M C 1-1-1 N M 6-7-11 N 8-9-13 End H, G, K, O a. Construct a network diagram. You can use either AOA or AON (see Example 5). 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. Page 779 Example 5 illustrates these computations. EXAMPLE 5 - Computing Expected Activity Times and Variances, and the Expected Duration and Standard Deviation of Each Path excel mhhe.com/stevenson14e The network diagram for a project is shown in the accompanying figure, with three time estimates for each activity. Activity times are in weeks. Do the following: a. Compute the expected time for each activity and the expected duration for each path. b. Identify the critical path. c. Compute the variance of each activity and the variance and standard deviation of each path. AOA diagram 3-4 Most likely time Optimistic time Pessimistic time 2-4-6 b 2-3-5 all AOA diagram Optimistic time Most likely time 2-4-6 b Pessimistic time 1-3-4 a 3-4-5 3-5-7 e 2-3-5 5-7-9 f d 2-3-6 g 165 4-6-8 h 3-4-6 AON diagram 1-3-4 2-4-6 2-3-5 AON diagram 1-3-4 2-4-6 2-3-5 a b 3-4-5 3-5-7 5-7-9 Start d e f Finish 2-3-6 4-6-8 3-4-6 h i SOLUTION TIMES to+4tm+tp 6 Path Activity to tm tp Path Total a-b-c a 1 3 4 2.83