Project Completion Time and Variance Analysis A project consists of ni | Operations Research 2081

Operations Research20815 marksNumerical: PERT expected time variancePERT network diagrams

Project Completion Time and Variance Analysis

A project consists of nine activities whose time estimates (in weeks) and other characteristics are given below. What is the expected project completion time and its variance?

Activities	A	B	C	D	E	F	G	H	I
Preceding activities	-	-	-	A	A	B,D	B,D	C,F	E
Optimistic time	2	6	6	2	11	8	3	9	4
Most likely time	4	6	12	5	14	10	6	15	10
Pessimistic time	6	6	24	8	23	12	9	27	16

[5]

Activity Predecessors $to$ $tm$ $tp$ -------------------------------------------- A - 2 4 6 B - 6 6 6 C - 6 12 24 D A 2 5 8 E A 11 14 23 F B, D 8 10 12 G B, D 3 6 9 H C, F 9 15 27 I E 4 10 16 $te = \frac{to + 4tm + tp}{6}, \qquad \sigma^2 = \left(\frac{tp - to}{6}\right)^2$ Activity $te$

Activity Predecessors $to$ $tm$ $tp$ -------------------------------------------- A - 2 4 6 B - 6 6 6 C - 6 12 24 D A 2 5 8 E A 11 14 23 F B, D 8 10 12 G B, D 3 6 9 H C, F 9 15 27 I E 4 10 16 $$te = \frac{to + 4tm + tp}{6}, \qquad \sigma^2 = \left(\frac{tp - to}{6}\right)^2$$ Activity $te$

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