Question

Table 1. Network information Activitv Description Immediate Predecessor Arrange financing Let Subcontracts Set and pour foundations Plumbin Framin Roofin Electrical wirin Installation of windows and doors Ductwork and insulation Sheetrock, paneling, an Installation of cabinets Brickin Outside trim Inside trim (including fixtures Paintin Floorin D.I F,G,H.J F.G,H.J hanging ?.? Table 2. Activity times in workdays Most Likelv 10 10 14 10 Activity Optimistic Pessimistic 12 16 18 12 12 24 12 4 10 10 10 10 20 18 24 16 27 24 18 14 12 25 10 14 12 23 10 10 4

a. Develop a report that presents a planned schedule and expected project completion time in
workdays. Include a project network in your report using MS Project.
b. Explain how does this project compared to the average project. The average duration for a
construction of a villa project normally takes 120 workdays.
c. Find the probability of finishing this project in 120 workdays?
d. Also find what expected completion time will ensure a 90% chance of completing the
project in 120 workdays?

Answer 1

a. Develop a report that presents a planned schedule and expected project completion time in
workdays. Include a project network in your report using MS Project.
Expected project completion time(te) is calculated using the formula te=(to+4*tm+tp)/6 where to is optimistic time, tp is pesimistic time and tm is most likely time.

Example: For activity id 1(that is activity A), to=8, tm=10, tp=12. Hence te=(to+4*tm+tp)/6 = (8+4*10+12)/6 = 10 workdays.

.0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559 2 1.4 0808 0793 0778 0764 .0749 .0735 .0721 0708 0694 0681 1.30968 0951 0934 .0918 0901 088 0869 0853 .0838 .0823 1.21151 .111 .1112 .1093 .1075.1056 .1038 .1020 1003 0985 1.1 1357 .1335 .1314 .1292 .1271 .1251.1230 .1210 .1190 .1170 1.0 .1587 .1562 .1539 .1515 .1492 .1469 1446 1423 .1401 1379 5 0.9.1841 .1814 .1788 .1762 1736. .1711 .1685 .1660 .1635 .1611 0.8 .2119 2090 .2061.2033 .2005.1977 1949 .1922 .1894.1867 0.7 .2420 .2389 2358 .2327 2296 .2266 2236 2206 2177 2148 0.6 .2743 .2709 .2676 .2643 .261 .2578 2546 .2514 .2483 2451 0.5 3085 3050 3015 .2981 2946 .2912 .2877 .2843 .2810 2776 9 0.4 3446 3409 3372 .3336 3300 .3264.3228 3192 3156 .3121 -0.31 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483 0.2 4207 4168 4129 4090 4052 4013 3974 .3936.3897 .3859 0.14602 4562 4522 4483 4443 444364 4325 4286 4247 0.0 5000 4960 4920 4880 4840 480 4761 472 468 4641 5 \r\n= (x-mean) / sd \r\n1.2815 = (120-mean)/11,333 \r\nmean - 120-1.2815 11.333-105.477 "",""error"":null,""modified"":1551902911,""source"":""automated""}"

Project network diagram generated from MS project is shown below:

The red coloured tasks shows the critical tasks, which gives the critical path with the longest working time to complete the project. The expected project completion time is therefore the sum of the expected workdays along the critical path A-B-C-E-I-J-K-N-O-P.

Total completion time = 10+10+14+8+14+22+12+14+12+6 = 122 workdays.

b. Explain how does this project compared to the average project. The average duration for a
construction of a villa project normally takes 120 workdays.

Along the critical path, the project takes an estimated total time of 122 workdays. But the average duration of a villa project is usually 120 workdays. This means that this project lags behind the average duration for completing a villa project, and takes extra 2 workdays.

c. Find the probability of finishing this project in 120 workdays?

$z=(x-mean)/sd$

where sd=standard deviation of critical path, x = 120 workdays(as given in question) , and

mean is the sum of all mean time estimates(te) along the critical path.

Therefore,

• mean = 122 workdays
• sd = 0.67+2+1.33+1.33+1.33+0.67+1.33+1.33+0.67+0.67 = 11.333
• x = 120 workdays.

$z=(120-122)/11.333 = -0.17647$

Now, from the cumulative distribution table, we can get the probability corresponding to the calculated z-value.

For z-value -0.17, the probability is 0.4325.

Hence, there is 43.25% probability of finishing this project in 120 workdays.

d. Also find what expected completion time will ensure a 90% chance of completing the
project in 120 workdays?

From the cumulative distribution table, for a probability value of 0.90 , the corresponding z-value is 1.281551.

$z=(x-mean)/sd$? , where

• Mean is the expected completion time which is unknown
• x = 120 workdays (given)
• sd = 0.67+2+1.33+1.33+1.33+0.67+1.33+1.33+0.67+0.67 = 11.333

Substituting the values in the formula, we get

$1.2815=(120-mean)/11.333$

$mean = 120 - 1.2815*11.333 = 105.477$

Hence, to ensure a 90% chance of completing the project in 120 workdays, the expected completion time is 105.47 workdays.