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Homework answers / question archive / Departement de science economique Department of Economics ENGINEERING ECONOMICS ECO 1192B Pink Assignment #2: Project Management C
Departement de science economique
Department of Economics
ENGINEERING ECONOMICS
ECO 1192B
Pink Assignment #2: Project Management
C.Théoret Winter 2021
A. Assignment Instructions
1. Completing an unallocated assignment will result in a zero (0%) score.
2. You will submit your assignment #2 answers on Brightspace on April
1 between 7 and 7:30 pm (Ottawa, Ontario time).
3. Assignment answers submitted late or by other means will be rejected.
4. The sequence of assignment questions in this document will be maintained on April 1 (i.e., no question scrambling)
5. Where appropriate
6. Please consult the appropriate Background Paper on Brightspace for assistance or seek assistance during my weekly office hour.
B. Project Management
You are planning the construction of a new restaurant. The duration (in weeks) and sequencing of major planning, construction and other activities are provided in the Table below.
|
Activities |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
Predecessor Activity |
-- |
1 |
1 |
1,3 |
2,3 |
3,4 |
2,5 |
5,6 |
6 |
7,8,9 |
|
Duration (weeks) |
5 |
6 |
7 |
4 |
6 |
7 |
4 |
6 |
7 |
6 |
|
Table 1 |
||||
|
Activity |
ES |
EF |
LS |
LF |
|
1 |
|
A |
|
|
|
2 |
B |
|
C |
|
|
3 |
|
D |
|
E |
|
4 |
|
|
F |
|
|
5 |
|
G |
|
|
|
6 |
|
|
H |
|
|
7 |
I |
|
J |
|
|
8 |
|
K |
L |
M |
|
9 |
N |
|
O |
P |
|
10 |
Q |
R |
S |
|
1. The number of weeks in cell Ain Table 1 is
2. The number of weeks in cell B in Table 1 is
3. The number of weeks in cell C in Table 1 is
4. The number of weeks in cell D in Table 1 is
5. The number of weeks in cell E in Table 1 is
6. The number of weeks in cell F in Table 1 is
7. The number of weeks in cell G in Table 1 is
8. The number of weeks in cell H in Table 1 is
9. The number of weeks in cell lin Table 1 is
10. The number of weeks in cell J in Table 1 is
11. The number of weeks in cell K in Table 1 is
12. The number of weeks in cell L in Table 1 is
13. The number of weeks in cell M in Table 1 is
14. The number of weeks in cell N in Table 1 is
15. The number of weeks in cell O in Table 1 is
16. The number of weeks in cell P in Table 1 is
17. The number of weeks in cell Q in Table 1 is
18. The number of weeks in cell R in Table 1 is
19. The number of weeks in cell S in Table 1 is
20. The slack (weeks) for activity 3 is
21. The slack (weeks) for activity 5 is
22. The slack (weeks) for activity 7 is
23. The slack (weeks) for activity 9 is
24. If the project is completed in the normal time (i.e., no “crashing” of activities), the activities on the critical path are
25. The project's normal completion time (weeks) is
|
Table 2 |
||||
|
Activity |
Normal Completion Time (weeks) |
Maximum weeks activities can be crashed |
Normal Cost/Week ($) |
Crashing Cost ($/Week) |
|
1 |
5 |
1 |
300 |
400 |
|
2 |
6 |
0 |
250 |
-- |
|
3 |
7 |
3 |
200 |
350 |
|
4 |
4 |
0 |
500 |
-- |
|
5 |
6 |
1 |
300 |
375 |
|
6 |
7 |
3 |
500 |
575 |
|
7 |
4 |
1 |
200 |
300 |
|
8 |
6 |
0 |
300 |
-- |
|
9 |
7 |
2 |
500 |
600 |
|
10 |
6 |
2 |
300 |
425 |
|
Example: If activity 7 were the first project activity to be crashed by 1 week, the project’s total completion cost would be the sum of the normal project cost + $300. |
||||
26. From Table 2, the cost ($) of the normal (before “crashing” any activity) completion of the project is d. 20,800
27. From Table 2, if the owners of the project wish to reduce the project's normal completion time by one (1) week, they should consider “crashing” activity
28. From Table 2, the completion cost of the project after “crashing” one (1) activity by one (1) week is
29. After reducing the project’s normal completion time by one (1) week (by “crashing” one (1) activity), the activities on the project's critical path will be
30. From Table 2, if the owners of the project want to reduce the project's normal completion time by a second week (after already “crashing” one activity by 1 week), they would “crash” activity
31. If the project’s normal completion time is reduced by two (2) weeks (due to activity “crashing’), its completion cost would be
The duration times of the 10 activities in the first part of the assignment were based on their most likely (probable) completion time. We know, however, that actual completion times can differ from the most likely completion times.
The most likely duration times are repeated in Table 3 along with optimistic (shorter) and pessimistic (longer) duration times.
32. The expected completion time (weeks) of the project (based on the activities on the critical path of a certain or risk-free environment) is between
33. The standard deviation (in weeks based on the activities on the critical path of a certain i.e., no risk environment) is between
34. Using a normal distribution, the probability (%) that the project will be completed in less than twenty-five (25) weeks (see the attached Table on the “Areas Under the Normal Curve” or use Excel’s Norm.Dist function) is
|
Table 3 |
|||||
|
Activity |
Optimistic Time (a) |
Most Likely Time (m) |
Pessimistic Time (b) |
Estimated Time |
Variance |
|
1 |
3 |
5 |
7 |
[3+7+(4*6)]/6 = 5 Weeks |
[(7-3)/6]2 = 0.4444 |
|
2 |
5 |
6 |
8 |
|
|
|
3 |
5 |
7 |
9 |
|
|
|
4 |
3 |
4 |
5 |
|
|
|
5 |
3 |
6 |
9 |
|
|
|
6 |
5 |
7 |
10 |
|
|
|
7 |
3 |
4 |
7 |
|
|
|
8 |
4 |
6 |
7 |
|
|
|
9 |
6 |
7 |
5 |
|
|
|
10 |
5 |
6 |
9 |
|
|
|
|
0 |
0.01 |
0.02 |
0.03 |
0.04 |
0.05 |
0.06 |
0.07 |
0.08 |
0.09 |
|
-3.4 |
0.000337 |
0.000349 |
0.000362 |
0.000376 |
0.00039 |
0.000404 |
0.000419 |
0.000434 |
0.00045 |
0.000466 |
|
-3.3 |
0.000483 |
0.000501 |
0.000519 |
0.000538 |
0.000557 |
0.000577 |
0.000598 |
0.000619 |
0.000641 |
0.000664 |
|
-3.2 |
0.000687 |
0.000711 |
0.000736 |
0.000762 |
0.000789 |
0.000816 |
0.000845 |
0.000874 |
0.000904 |
0.000935 |
|
-3.1 |
0.000968 |
0.001001 |
0.001035 |
0.00107 |
0.001107 |
0.001144 |
0.001183 |
0.001223 |
0.001264 |
0.001306 |
|
-3 |
0.00135 |
0.001395 |
0.001441 |
0.001489 |
0.001538 |
0.001589 |
0.001641 |
0.001695 |
0.00175 |
0.001807 |
|
-2.9 |
0.001866 |
0.001926 |
0.001988 |
0.002052 |
0.002118 |
0.002186 |
0.002256 |
0.002327 |
0.002401 |
0.002477 |
|
-2.8 |
0.002555 |
0.002635 |
0.002718 |
0.002803 |
0.00289 |
0.00298 |
0.003072 |
0.003167 |
0.003264 |
0.003364 |
|
-2.7 |
0.003467 |
0.003573 |
0.003681 |
0.003793 |
0.003907 |
0.004025 |
0.004145 |
0.004269 |
0.004396 |
0.004527 |
|
-2.6 |
0.004661 |
0.004799 |
0.00494 |
0.005085 |
0.005234 |
0.005386 |
0.005543 |
0.005703 |
0.005868 |
0.006037 |
|
-2.5 |
0.00621 |
0.006387 |
0.006569 |
0.006756 |
0.006947 |
0.007143 |
0.007344 |
0.007549 |
0.00776 |
0.007976 |
|
-2.4 |
0.008198 |
0.008424 |
0.008656 |
0.008894 |
0.009137 |
0.009387 |
0.009642 |
0.009903 |
0.01017 |
0.010444 |
|
-2.3 |
0.010724 |
0.011011 |
0.011304 |
0.011604 |
0.011911 |
0.012224 |
0.012545 |
0.012874 |
0.013209 |
0.013553 |
|
-2.2 |
0.013903 |
0.014262 |
0.014629 |
0.015003 |
0.015386 |
0.015778 |
0.016177 |
0.016586 |
0.017003 |
0.017429 |
|
-2.1 |
0.017864 |
0.018309 |
0.018763 |
0.019226 |
0.019699 |
0.020182 |
0.020675 |
0.021178 |
0.021692 |
0.022216 |
|
-2 |
0.02275 |
0.023295 |
0.023852 |
0.024419 |
0.024998 |
0.025588 |
0.02619 |
0.026803 |
0.027429 |
0.028067 |
|
-1.9 |
0.028717 |
0.029379 |
0.030054 |
0.030742 |
0.031443 |
0.032157 |
0.032884 |
0.033625 |
0.03438 |
0.035148 |
|
-1.8 |
0.03593 |
0.036727 |
0.037538 |
0.038364 |
0.039204 |
0.040059 |
0.04093 |
0.041815 |
0.042716 |
0.043633 |
|
-1.7 |
0.044565 |
0.045514 |
0.046479 |
0.04746 |
0.048457 |
0.049471 |
0.050503 |
0.051551 |
0.052616 |
0.053699 |
|
-1.6 |
0.054799 |
0.055917 |
0.057053 |
0.058208 |
0.05938 |
0.060571 |
0.06178 |
0.063008 |
0.064255 |
0.065522 |
|
-1.5 |
0.066807 |
0.068112 |
0.069437 |
0.070781 |
0.072145 |
0.073529 |
0.074934 |
0.076359 |
0.077804 |
0.07927 |
|
-1.4 |
0.080757 |
0.082264 |
0.083793 |
0.085343 |
0.086915 |
0.088508 |
0.090123 |
0.091759 |
0.093418 |
0.095098 |
|
-1.3 |
0.0968 |
0.098525 |
0.100273 |
0.102042 |
0.103835 |
0.10565 |
0.107488 |
0.109349 |
0.111232 |
0.113139 |
|
-1.2 |
0.11507 |
0.117023 |
0.119 |
0.121 |
0.123024 |
0.125072 |
0.127143 |
0.129238 |
0.131357 |
0.1335 |
|
-1.1 |
0.135666 |
0.137857 |
0.140071 |
0.14231 |
0.144572 |
0.146859 |
0.14917 |
0.151505 |
0.153864 |
0.156248 |
|
-1 |
0.158655 |
0.161087 |
0.163543 |
0.166023 |
0.168528 |
0.171056 |
0.173609 |
0.176186 |
0.178786 |
0.181411 |
|
-0.9 |
0.18406 |
0.186733 |
0.18943 |
0.19215 |
0.194895 |
0.197663 |
0.200454 |
0.203269 |
0.206108 |
0.20897 |
|
-0.8 |
0.211855 |
0.214764 |
0.217695 |
0.22065 |
0.223627 |
0.226627 |
0.22965 |
0.232695 |
0.235762 |
0.238852 |
|
-0.7 |
0.241964 |
0.245097 |
0.248252 |
0.251429 |
0.254627 |
0.257846 |
0.261086 |
0.264347 |
0.267629 |
0.270931 |
|
-0.6 |
0.274253 |
0.277595 |
0.280957 |
0.284339 |
0.28774 |
0.29116 |
0.294599 |
0.298056 |
0.301532 |
0.305026 |
|
-0.5 |
0.308538 |
0.312067 |
0.315614 |
0.319178 |
0.322758 |
0.326355 |
0.329969 |
0.333598 |
0.337243 |
0.340903 |
|
-0.4 |
0.344578 |
0.348268 |
0.351973 |
0.355691 |
0.359424 |
0.363169 |
0.366928 |
0.3707 |
0.374484 |
0.37828 |
|
-0.3 |
0.382089 |
0.385908 |
0.389739 |
0.39358 |
0.397432 |
0.401294 |
0.405165 |
0.409046 |
0.412936 |
0.416834 |
|
-0.2 |
0.42074 |
0.424655 |
0.428576 |
0.432505 |
0.436441 |
0.440382 |
0.44433 |
0.448283 |
0.452242 |
0.456205 |
|
-0.1 |
0.460172 |
0.464144 |
0.468119 |
0.472097 |
0.476078 |
0.480061 |
0.484047 |
0.488034 |
0.492022 |
0.496011 |
|
0 |
0.5 |
0.503989 |
0.507978 |
0.511966 |
0.515953 |
0.519939 |
0.523922 |
0.527903 |
0.531881 |
0.535856 |
|
0.1 |
0.539828 |
0.543795 |
0.547758 |
0.551717 |
0.55567 |
0.559618 |
0.563559 |
0.567495 |
0.571424 |
0.575345 |
|
0.2 |
0.57926 |
0.583166 |
0.587064 |
0.590954 |
0.594835 |
0.598706 |
0.602568 |
0.60642 |
0.610261 |
0.614092 |
|
0.3 |
0.617911 |
0.62172 |
0.625516 |
0.6293 |
0.633072 |
0.636831 |
0.640576 |
0.644309 |
0.648027 |
0.651732 |
|
0.4 |
0.655422 |
0.659097 |
0.662757 |
0.666402 |
0.670031 |
0.673645 |
0.677242 |
0.680822 |
0.684386 |
0.687933 |
|
0.5 |
0.691462 |
0.694974 |
0.698468 |
0.701944 |
0.705401 |
0.70884 |
0.71226 |
0.715661 |
0.719043 |
0.722405 |
|
0.6 |
0.725747 |
0.729069 |
0.732371 |
0.735653 |
0.738914 |
0.742154 |
0.745373 |
0.748571 |
0.751748 |
0.754903 |
|
0.7 |
0.758036 |
0.761148 |
0.764238 |
0.767305 |
0.77035 |
0.773373 |
0.776373 |
0.77935 |
0.782305 |
0.785236 |
|
0.8 |
0.788145 |
0.79103 |
0.793892 |
0.796731 |
0.799546 |
0.802337 |
0.805105 |
0.80785 |
0.81057 |
0.813267 |
|
0.9 |
0.81594 |
0.818589 |
0.821214 |
0.823814 |
0.826391 |
0.828944 |
0.831472 |
0.833977 |
0.836457 |
0.838913 |
|
1 |
0.841345 |
0.843752 |
0.846136 |
0.848495 |
0.85083 |
0.853141 |
0.855428 |
0.85769 |
0.859929 |
0.862143 |
|
1.1 |
0.864334 |
0.8665 |
0.868643 |
0.870762 |
0.872857 |
0.874928 |
0.876976 |
0.879 |
0.881 |
0.882977 |
|
1.2 |
0.88493 |
0.886861 |
0.888768 |
0.890651 |
0.892512 |
0.89435 |
0.896165 |
0.897958 |
0.899727 |
0.901475 |
|
1.3 |
0.9032 |
0.904902 |
0.906582 |
0.908241 |
0.909877 |
0.911492 |
0.913085 |
0.914657 |
0.916207 |
0.917736 |
|
1.4 |
0.919243 |
0.92073 |
0.922196 |
0.923641 |
0.925066 |
0.926471 |
0.927855 |
0.929219 |
0.930563 |
0.931888 |
|
1.5 |
0.933193 |
0.934478 |
0.935745 |
0.936992 |
0.93822 |
0.939429 |
0.94062 |
0.941792 |
0.942947 |
0.944083 |
|
1.6 |
0.945201 |
0.946301 |
0.947384 |
0.948449 |
0.949497 |
0.950529 |
0.951543 |
0.95254 |
0.953521 |
0.954486 |
|
1.7 |
0.955435 |
0.956367 |
0.957284 |
0.958185 |
0.95907 |
0.959941 |
0.960796 |
0.961636 |
0.962462 |
0.963273 |
|
1.8 |
0.96407 |
0.964852 |
0.96562 |
0.966375 |
0.967116 |
0.967843 |
0.968557 |
0.969258 |
0.969946 |
0.970621 |
|
1.9 |
0.971283 |
0.971933 |
0.972571 |
0.973197 |
0.97381 |
0.974412 |
0.975002 |
0.975581 |
0.976148 |
0.976705 |
|
2 |
0.97725 |
0.977784 |
0.978308 |
0.978822 |
0.979325 |
0.979818 |
0.980301 |
0.980774 |
0.981237 |
0.981691 |
|
2.1 |
0.982136 |
0.982571 |
0.982997 |
0.983414 |
0.983823 |
0.984222 |
0.984614 |
0.984997 |
0.985371 |
0.985738 |
|
2.2 |
0.986097 |
0.986447 |
0.986791 |
0.987126 |
0.987455 |
0.987776 |
0.988089 |
0.988396 |
0.988696 |
0.988989 |
|
2.3 |
0.989276 |
0.989556 |
0.98983 |
0.990097 |
0.990358 |
0.990613 |
0.990863 |
0.991106 |
0.991344 |
0.991576 |
|
2.4 |
0.991802 |
0.992024 |
0.99224 |
0.992451 |
0.992656 |
0.992857 |
0.993053 |
0.993244 |
0.993431 |
0.993613 |
|
2.5 |
0.99379 |
0.993963 |
0.994132 |
0.994297 |
0.994457 |
0.994614 |
0.994766 |
0.994915 |
0.99506 |
0.995201 |
|
2.6 |
0.995339 |
0.995473 |
0.995604 |
0.995731 |
0.995855 |
0.995975 |
0.996093 |
0.996207 |
0.996319 |
0.996427 |
|
2.7 |
0.996533 |
0.996636 |
0.996736 |
0.996833 |
0.996928 |
0.99702 |
0.99711 |
0.997197 |
0.997282 |
0.997365 |
|
2.8 |
0.997445 |
0.997523 |
0.997599 |
0.997673 |
0.997744 |
0.997814 |
0.997882 |
0.997948 |
0.998012 |
0.998074 |
|
2.9 |
0.998134 |
0.998193 |
0.99825 |
0.998305 |
0.998359 |
0.998411 |
0.998462 |
0.998511 |
0.998559 |
0.998605 |
|
3 |
0.99865 |
0.998694 |
0.998736 |
0.998777 |
0.998817 |
0.998856 |
0.998893 |
0.99893 |
0.998965 |
0.998999 |
|
3.1 |
0.999032 |
0.999065 |
0.999096 |
0.999126 |
0.999155 |
0.999184 |
0.999211 |
0.999238 |
0.999264 |
0.999289 |
|
3.2 |
0.999313 |
0.999336 |
0.999359 |
0.999381 |
0.999402 |
0.999423 |
0.999443 |
0.999462 |
0.999481 |
0.999499 |
|
3.3 |
0.999517 |
0.999534 |
0.99955 |
0.999566 |
0.999581 |
0.999596 |
0.99961 |
0.999624 |
0.999638 |
0.999651 |
|
3.4 |
0.999663 |
0.999675 |
0.999687 |
0.999698 |
0.999709 |
0.99972 |
0.99973 |
0.99974 |
0.999749 |
0.999758 |
|
3.5 |
0.999767 |
0.999776 |
0.999784 |
0.999792 |
0.9998 |
0.999807 |
0.999815 |
0.999822 |
0.999828 |
0.999835 |
