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ChaPter 3 • ProjeCt management 81

Eligible Activity Time for Each Path Cost Cumulative Figure 3.26
Activities Chosen 22 19 19 16 Cost Using expediting to minimize
project time.
A, B, D, or I B 21 18 19 16 $ 500 $ 500

A, B, D, or I B 20 17 19 15 500 1000
A, D, or I I 19 17 18 15 600 1600

A or D A 18 16 18 15 800 2400
A and C, or D D 17 16 17 15 1000 3400

A and C, or D D 16 16 16 15 1000 4400
A and C A and C 15 15 15 14 1200 5600

The maximum number of weeks each activity can be reduced is the difference between the
expected time and its crash time. For example, activity B, administering questionnaires, could
be reduced from four weeks to two weeks at a cost of $500 per week, but it cannot be reduced
less than 2 weeks; activity H, preparing the proposal, cannot be reduced because it is already at
its crash time.
The expediting analysis for this example is provided in Figure 3.26. The expediting process
takes place one step at a time, until it is impossible to expedite any further. The columns in the table
include eligible activities (tasks that are on the critical path and can be reduced by expediting), the
activity chosen (because it is the cheapest alternative), the time it currently takes to complete each
of the paths, the cost of expediting the chosen activity, and finally the cumulative cost.
In the first step, the critical path is 10–20–30–50–60–70–80, so the eligible activities are
A, B, D, and I. Activities G and H are also on the critical path, but they are already at their
crash times and are consequently ineligible for expediting. The cheapest alternative is to expe-
dite activity B by one day, which reduces the first path from 22 to 21 weeks and the second from
19 to 18 weeks; the third and fourth paths are not affected by the reduction since activity B is not
on either of those paths.
The critical path, and therefore the entire project, is reduced from 22 to 21 weeks (circled on
the table). We can repeat this reduction and reduce the project time by another week.
When activity B reaches its crash time, another activity must be chosen. Row 3 in the table
shows that activities A, D, and I are eligible, and activity I is the cheapest alternative. Reducing
activity I reduces not only the critical path but all paths because it is common to all of them.
In the fourth step, activity A is chosen, reducing paths 1 and 2, but as a result, there are now
two critical paths. This implies that any reduction of the project time will take place only if both
of the critical paths are reduced at the same time.
We can shorten both paths in the fifth and sixth steps by choosing either a combination of
activities A and C (one activity from each of the critical paths) or activity D (an activity common
to both critical paths). Reducing activity D by 2 days shortens the paths to 16, 16, 16, and 15
days, respectively, and now there are three critical paths.
Finally, when activity D reaches its crash time, the only available choice is a combination
of activities A and C. The minimum project time is therefore 15 weeks, obtainable by reducing
activity A by 2 days, activity B by 2 days, activity C by 1 day, activity D by 2 days, and activity
I by one day, at a total cost of $5,600.
This example describes all-out expediting to obtain the minimum project time at any cost.
But a systems analyst may be faced with a budget. In our example, a budget of $4,000 would
result in expediting up to and including step 5. The project would be shortened from 22 to 17
weeks, at a cost of $3,400.
Another possible criterion would be the net amount that could be saved if the project were
shortened. Suppose that in the above example, the analyst would save $750 per week, mostly
consisting of the opportunities available for the project team to begin new projects sooner. In
this case, expediting would take place until step 3, since the incremental cost of step 4 ($800 for
expending activity A) would exceed the $750 saved.