A partially solved PERT problem is detailed in the table below. Times are given in weeks. Activity Immediate Predecessor(s) Optimistic Time Most Likely Time Pessimistic Time A -- 5 11 14 B - 3 3 9 C -- 6 10 14 D A, B 3 5 7 E B 4 6 11 F C 6 8 13 G D, E 2 4 6 H F 3 3 9 I G 2 4 6 J H 4 7 9 K I, J 4 7 8 a) Calculate the expected duration (D), and variance of each activity. b) Calculate ES, EF, LS, LF, S for each activity.
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0 weeks, Variance = (14 - 4) / 6 = 1.67 - For Activity B: D = (4 + 0 + 10) / 6 = 2.33 weeks, Variance = (10 - 4) / 6 = 1.0 - For Activity C: D = (0 + 0 + 10) / 6 = 1.67 weeks, Variance = (10 - 0) / 6 = 1.67 - For Activity D: D = (4 + 5 + 14) / 6 = 4.5 weeks, Show more…
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Question 3: (a) Explain the following terms in PERT: i. Optimistic time ii. Normal time iii. Pessimistic time iv. Expected time v. Variance in relation to activities. (b) A project schedule has the following characteristics: Activity Time (weeks) Activity Time (weeks) 1-2 4 5-6 4 1-3 1 5-7 8 2-4 1 6-8 1 3-4 1 7-8 2 3-5 6 8-10 5 4-9 5 9-10 7 i. Construct the network ii. Compute the earliest time (E) and latest time (L) iii. Find the critical path
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Time of Traffic Fatality In Exercise 51 of the previous section, the probability density function for the number of fatal traffic accidents was found to be $$S(t)=\frac{1}{91,762}\left(-2.416 t^{3}+90.91 t^{2}-846.8 t+4880\right)$$ where $t$ is the number of hours since midnight on $[0,24]$. Calculate the expected time of day at which a fatal accident will occur. Source: The National Highway Traffic Safety Administration.
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