Aoa Problems with Solutions
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 %.
Interpolation
1.41 ………..0.9207
1.414 …………. p
1.42 ………..0.9222
(1.414 – 1.41/(1.42- 1.41) =(p – 0.9207)/(0. 9222- 0. 9207)
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Therefore, there is 92.13% probability that the project will be finished in 30 weeks.
0O0
2. A reactor and storage tank are interconnected by a 3” insulated process line that needs periodic replacement. There are valves along the lines and at the terminals and these need replacing as well. No pipe and valves are in stock. Accurate, as built, drawings exist and are available. You are the maintenance and construction superintendent responsible for this project. The works engineer has requested your plan and schedule for a review with the operating supervision. The plant methods and standards section has furnished the
[pic]
[pic]
SOLUTION:
[pic][pic]
[pic]
(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 %.
Interpolation
1.41 ………..0.9207
1.414 …………. p
1.42 ………..0.9222
(1.414 – 1.41/(1.42- 1.41) =(p – 0.9207)/(0. 9222- 0. 9207)
[pic]
Therefore, there is 92.13% probability that the project will be finished in 30 weeks.
0O0
2. A reactor and storage tank are interconnected by a 3” insulated process line that needs periodic replacement. There are valves along the lines and at the terminals and these need replacing as well. No pipe and valves are in stock. Accurate, as built, drawings exist and are available. You are the maintenance and construction superintendent responsible for this project. The works engineer has requested your plan and schedule for a review with the operating supervision. The plant methods and standards section has furnished the