PERT EXAMPLE 2 4 6 (C,11,4) (F,6,4/9) (A,12,4) (D,14,1/9) (G,2,0) (1,4,4/9) 8 (B,16,1) (J,2,1/9) 3 5 7 (E,9,1) (H,7,1/9) TE earliest event occurrence time TL=latest allowable event occurrence time ES Event Slack TE TL ES (, o) ACTIVITY DURATIONS IN PERT NETWORK . Beta Distribution is used to model activity durations Mean and standard deviation of the beta distribution are approximated by the following equations a+4m+b 6 b-a 6 oject ivan PERT EXAMPLE What is the probability of the Project ending before 40 days? 2 4 6 (C,11,4) (F,6,4/9) 12 19 7 30 30 0 36 36 0 (1,4,4/9) (A,12,4) 8 1 (D,14,1/9) (G,2,0) 40 40 0 0 II 0 0 (B,16,1) (J,2,1/9) 5 16 16 (E,9,1) 0 25 31 6 7 32 38 (H,7,1/9) 6 Path (t) Activities Mean Variance P(t 40) 1-3-4-6-8 X B-D-F-I 40 40 2 P(z 40-40) = 0.5 -> 0.9906*0.5 1-2-4-6-8 Y 33 88/9 P Z A-C-F-I 40 33 88/9 0.9906 1-3-5-6-8 Z 31 24/9 B-E-G-I 1-3-5-7-8 W 34 22/9 B-E-H-J Events Z and W can be neglected since: Fy(a)Fx(a) 313*Sqrt(24/9)=35.7 < 40 34+3 Sqrt(22/9)38.47 < 40 Fz(a) Min{ Fy (a), Fx (a)} P(t 40) Min (0.5, 0.9906) 0.4953 P(t40) 0.5 PERT MERGE BIAS S X j Y Fz(a) = P(Z a) P(Y a) P(X a) If Pxy 1 then Fz(a) Min{ Fy (a), Fx (a)} Hence, Fy(a)Fx(a) Fz(a) Min{ Fy(a), Fx (a)} Lower bound LB (when X & Y are independent) Upper bound UB (when X & Y are dependent) 1. Data for a simplified PERT network are given below: 10 B 15 20 E 25 30 Time Estimates (days) M 35 N 45 40 i j ACT a m b 5 10 A 7 10 16 5 15 B 2 5 6 10 20 C 5 7 11 10 25 E 8 10 11 15 25 dl 0 0 0 15 30 F 7 10 11 20 35 G 4 6 7 25 35 L 3 5 11 30 35 d2 0 0 0 30 40 M 4 7 9 35 45 N 3 6 11 40 45 P 5 6 7 a. After calculating the mean and standard deviation for each activity duration, calculate Early Event Times (TE) and Late Event Times (TL) for all nodes. b. Determine the PERT "critical path(s)" and the mean and standard deviation for the project duration. c. Determine the probability of completing the project in 31 days or less. d. Determine the probability of completing the project in 33 days or more. Determine the probability of reaching event/node 35 in 24 days or less.