1. Three different time estimates for various activities of a project are given in the below table. Construct a PERT network and find out (a) The earliest possible time (TE) to complete the different activities, (b) The latest allowable time (TL) for them, (c) The slack values, (d) The critical paths, and (e) The probability factor for completing the project in 30 weeks.

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SOLUTION:

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(iv) Critical Path

1–2–4–6–7–9–10 = 28 weeks.

Vcp = 2 and σcp = 1.41

(v) The probability factor for completing the project in 30 weeks.

Z = (X – μ)/σ

where X = 30 weeks, μ = 28 weeks and σCP = 1.41

Hence,

Z = (30 28)/141 = 1.41

Z is the number of standard deviations by which X exceeds μ

μ = Te is the total project duration, and

X = due or scheduled date or time

From the table of Standard Normal Distribution Function, the corresponding percentage probabilities

are given as follows:

For Z = 1.41 the probability is 92.07 % and for Z = 1.42 the probability is 92.22 %.

Therefore, there is 92.13% probability that the project will be finished in 30 weeks.

0O0

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