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CONSIDERING TIME–COST TRADE-OFFS 393

Worst Best
case Likely case Expected
Activity duration duration duration duration Variance
A 6 5 3 4.833333 0.25
B 6 4 2 4 0.444444
C 7 6 5 6 0.111111
D 10 9 7 8.833333 0.25
E 6 4 2 4 0.444444
F 3 2 1 2 0.111111
G 10 8 5 7.833333 0.694444
H 10 8 6 8 0.444444
I 5 4 3 4 0.111111

We can then construct the network diagram using the Expected durations to identify the critical path. This is
shown below. From the diagram we see that the Expected completion time is 43.5 days with all activities
critical except for E and F. However, we can go one stage further. The contractor works five days each week so
the hotel’s summer season effectively starts in 45 working days’ time (nine weeks x five). We can calculate the
variance of the critical activities at 2.31 and the standard deviation at 1.51.We can then calculate the probability
that the project will be completed within 45 working days:

43:5 45
Z ¼ ¼ 0:99
1:51
From the Normal probability table we see this has a probability associated with it of 0.3389. Therefore the
probability that the project will be completed within 45 days is 0.84 (0.5+0.3389) or 84 per cent. So we can tell
the hotel that, based on the information given, there is an 84 per cent chance the project will be finished before
the summer season starts. If this is seen as unacceptable, we can advise the hotel to consider paying a bonus
to the contractor for crashing critical activities. We have no information on this at present but it would not be
difficult to obtain from the contractor any extra costs incurred in speeding up parts of the project. Clearly, the
hotel would then have to assess whether these extra crash costs were worthwhile.

E 14.8 18.8 F 23.7 25.7
4 33.5 37.5 2 37.5 39.5

A 0 4.8 B 4.8 8.8 C 8.8 14.8 I 32.5 43.5
Start Finish
4.8 0 4.8 4 4.8 8.8 6 8.8 14.8 4 32.5 43.5
D 14.8 23.7 G 23.7 31.5 H 31.5 39.5
8.8 14.8 23.7 7.8 23.7 31.5 8 31.5 39.5

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