CPM Terminology and Method
Probabilistic Times and Meeting Due Dates
Management 120
1
Formula Sheets
Costs and Crashing Activities
NT = normal time = time to complete activity under normal conditions
NC = normal cost = cost to complete under normal conditions
CT = crash time = shortest possible time to complete activity
CC = crash cost = cost to complete activity in the shortest possible time
Maximum time reduction = NT - CT
Cost to crash per period = (CC-NC) / (NT-CT)
Example cost and crashing data table:
Normal
Normal
Time
Cost
Activity
(NC)
(NC)
A
12
12,000
B
9
50,000
C
10
4,000
.
.
.
.
.
.
.
.
.
Crash
Time
(CT)
11
7
5
.
.
.
Crash
Cost
(CC)
13,000
64,000
7,000
.
.
.
Maximum
Time
Reduction
1
2
5
.
.
.
Cost to
Crash per
Period
1,000
7,000
600
.
.
.
Minimum Time and Cost Schedules
Finding the minimum time schedule at least cost:
1. Set all times to crash time and find the critical path and project completion time.
2. Find the non-critical activity with the most expensive crash cost per period.
3. Relax it as much as possible up to the normal time or until no slack is left.
4. Repeat steps 2 and 3 until no more non-critical activities can be relaxed.
Finding the minimum cost schedule:
[Indirect costs are those costs incurred when the project is in progress, independent of which
activity or activities are being performed. A late penalty cost is one kind of indirect cost. Direct
costs are the costs of the activities themselves.]
1. List all paths in the network and their total normal times.
2. Find the activity (or activities) on the critical path(s) that is (are) least expensive per
period to crash.
3. If the cost to crash per period is more than the savings in indirect cost from reducing
the project time, then you are finished, unless you must meet a given due date. If cost is
less, or if due date must be met, continue with step 4.
4. Reduce the time on this activity either to its maximum time reduction or until it causes
another path to also become critical. (If more than one path is critical, it may be
necessary to reduce the time for an activity on each path simultaneously.)
5. Go back to step 2.
Management 120
2
Formula sheets