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Calculate the project duration
written 8.3 years ago by gravatar for teamques10 teamques10 ★ 68k modified 2.8 years ago by gravatar for sagarkolekar sagarkolekar ★ 11k

A PERT network details are as given below.

Activity T0 Tm Tp(days all)
10-20 3 6 9
10-30 3 6 8
20-40 6 8 10
20-50 10 12 15
30-50 4 6 7
40-70 8 10 12
40-60 8 10 11
50-60 3 5 8
60-70 4 8 12
Z -3 -2 -1 0 1 2 3
P % 0.13 2.28 15.87 50 84.13 97 99

i) Calculate the project duration for 50% probability.

ii) Work out probability of completion in 22 days.
construction management
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written 8.3 years ago by gravatar for teamques10 teamques10 ★ 68k

Step :1

Activity $T_0$ $T_m$ $T_p$ $t_e = \frac{t_0 + 4t_m + t_p}{6}$ $\sigma = \frac{t_p - t_0}{6}$ $\sigma^2$
10-20 3 6 9 6 1 1
10-30 3 6 8 5.83
20-40 6 8 10 8 0.66 0.435
20-50 10 12 15 12.16
30-50 4 6 7 5.83
40-70 8 10 12 10
40-60 8 10 11 9.83 0.5 0.25
50-60 3 5 8 5.16
60-70 4 8 12 8 1.33 1.768
$\sum \sigma^2 = 3.45$

Step : 2

enter image description here

Project duration=31.83 days

Critical path = 10-20-40-70 = 10-20-40-60-70

Step : 3

  1. For probability , the Scheduled time will be same as that of project duration.

    ∴Project duration=31.83 Days.

  2. Probability of completing the project in 22 Days

    z = $\frac{\text{scheduled time-project duration}}{\epsilon}$

    S.T.= 22 Days

    P.D.= 31.83 Days

    $∈ = \sqrt{σ^2}= \sqrt{3.45}=1.85$

    z = $\frac{22-31.38}{1.85} = -5.31$

    ∴ Extrapolating Z for probability,

    enter image description here

    $\boxed{P \% = -5.09 \% \lt 0}$

    Hence the project cannot be completed in 22 days.
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