Question

16) A partially solved PERT problem is detailed in the table below. Times are given in weeks. Optimisti Activity Preceding Time Probable Pessimistie Expected Time Time Time Variance 10 8 19 20 - 니다 4-ww0 8 16 14 1 2.79 276 G + - 5 (a) Calculate the expected time and variance for each activity. Enter these values in the appropriate columns in the table above. (b) Which activities form the critical path? (c) What is the estimated time of the critical path? (d) What are the project variance and the project standard deviation? (e) What is the probability of completion of the project before week 42.

Answer 1

(a) For each activity, find the expected mean time (u) = (a + 4m +b)/6, and Variance o = (b - a)?/3 Activity Immediate predecessor 7 10 19 Mean Variance time (u) (6) 114.00 3 1.00 12 1.78 1.36 0.44 5.5 0.44 600 mm 3 2 8 | 0.11 1.00 2.78 2.78 1.00 1 2 5 14 8 7 5

(b)

Find the Early Start (ES), Early Finish (EF), Late Start (LS), Late Finish (LF) times and Slack for each activity. Early Start is calculated by forward pass method as latest of the predecessors Early Finish. Late Finish is calculated using reverse pass method as earliest of the successors Late Start. Early Finish = Early Start + Activity Duration Late Start=Late Finish - Activity Duration Slack = Late Finish - Early Finish, or Late Start - Early Start Activity Predecessor variance (?) LS LF Slack Expected Time (u) 11 Successor Critical Activity Critical 19 11 11 B,C,D 14 0 3.5 2.5 | 16 | 12 1 1.78 1.36 0.44 0.44 11 11 14 23 2 16.5 20 Critical IY 0 14 14.5 13.5 11 29.5 17.5 25.5 16.5 19.5 28.5 35.5 22 26 17.5 25.5 16.5 35.5 25.5 28.5 19.5 28.5 35.5 40.5 15.5 3.5 2.5 0.11 19.5 - 18 2.78 2.78 23 16.5 19.5 28.5 35.5 Critical Critical Critical Critical 28.5 35.5 40.5 14

Activities A, D, H, I, J, K form the critical path

(c) Estimated time of the critical path is: 40.5 week

(d) Project variance = sum of variances of activities that form the critical path

= 4+1.36+1+2.78+2.78+1

= 12.92

Project standard deviation = square root of variance

= sqrt(12.92)

= 3.59 weeks

(e)

For target week 42,

z value = (42 - estimated time of critical path) / Standard deviation

= (42 - 40.5)/3.59

= 0.4178

P(z<0.4178) = NORMSDIST(0.4178)

= 0.662

or 66.2 %

Probability of completion of the project before week 42 = 66.2 %