The Denver Iron & Steel Company is expanding its operations to include a new dri

Question

The Denver Iron & Steel Company is expanding its operations to include a new drive-in station. The weigh station w ill be a heated-air-conditioned building with a large floor and sma office. The large room will have the scales, a 15-foot counter, and several display cases for i s equipment. Before erection of the building, the project manager evaluated the project using probabilistic modeling. The following activities with their corresponding times (in weeks) were a. Draw the network showing expected activity durations for this project using the AIB method. b.Find the critical path and the expected completion time for the project. c.Sketch the normal distribution for this project showing the (-3_sigma,.-2_sigma,-l_sigma, l_sigma, 2_sigma, 3_sigma) points on the curve. d.What is the 2.5sigma duration for completing the project?

Explanation / Answer

AIB stands for Activity in Box and the method uses the forward pass for calculation of earliest start times and backward pass for calculating the latest finish times for all the activities. Based on the times slacks and or floats are calculated to determine tha critical activities and hence the critical path.

Project duration is supposed to follow normal distribution with mean 66.33 and standard deviation=2.71

2.5sigma = 2.5*2.71=6.78 approx and the corresponding project duration is 73.11 approx

Activity Activity duration estimates Prec.Act. Exp.Time Variance Earliest Latest To Tm Tp To+4Tm+Tp/6 Tp-To/6 Start Finish Start Finish Slack 1 8 10 13 -- 10.17 0.83 0.00 10.17 11.66 21.83 11.66 2 5 6 8 -- 6.17 0.50 0.00 6.17 0.00 6.17 0.00 3 13 15 21 2 15.67 1.33 6.17 21.83 6.16 21.83 0.00 4 10 12 14 1,3 12.00 0.67 21.83 33.83 21.83 33.83 0.00 5 11 20 30 4 20.17 3.17 33.83 54.00 33.83 54.00 0.00 6 4 5 8 5 5.33 0.67 54.00 59.33 58.00 63.33 4.00 7 2 3 4 5 3.00 0.33 54.00 57.00 54.00 57.00 0.00 8 4 6 10 7 6.33 1.00 57.00 63.33 57.00 63.33 0.00 9 2 3 4 8,6 3.00 0.33 63.33 66.33 63.33 66.33 0.00 Critical path is made up of 2--3--4--5--7--8--9 with expected duration 66.33 Only activities 1 and 6 are non critical Variance of the project duration= sum of the variances of critical activities 7.33 S.D.= 2.708013

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