Operations and Supply Chain Management The Core

PROJECTS chapter 5 147
Example of Time–Cost Trade-Off Procedure
exhibit 5.10
Step 1. Prepare CPM Diagram with Activity Costs
Step 2. Determine Cost per Unit of Time
CT
NT
NC
CC
2, 1
A
$6, $10
CC Crash cost
CT Crash time
NC Normal cost
NT Normal time
5, 2
B
$9, $18
4, 3
C
$6, $8
0
0
3, 1
D
$5, $9
Activity
cost
$10
8
6
CC, CT
NC, NT
Activity A
1 2 3 4
Time
Step 3. Compute the Critical Path
2 7
B(5)
A(2)
2
2
2
2
3
C(4)
7
6
7
7
7
D(3)
10
10
Excel: Project
Management
1. Prepare a CPM-type network diagram. For each activity, this diagram should list:
a. Normal cost (NC): the lowest expected activity costs. (These are the lesser of
the cost figures shown under each node in Exhibit 5.10.)
b. Normal time (NT): the time associated with each normal cost.
c. Crash time (CT): the shortest possible activity time.
d. Crash cost (CC): the cost associated with each crash time.
2. Determine the cost per unit of time (assume days) to expedite each activity. The
relationship between activity time and cost may be shown graphically by plotting
CC and CT coordinates and connecting them to the NC and NT coordinates by a
concave, convex, or straight line—or some other form, depending on the actual cost
structure of activity performance, as in Exhibit 5.10. For activity A, we assume a
linear relationship between time and cost. This assumption is common in practice
and helps us derive the cost per day to expedite because this value may be found
directly by taking the slope of the line using the formula Slope = (CC − NC) ÷
(NT − CT). (When the assumption of linearity cannot be made, the cost of expediting
must be determined graphically for each day the activity may be shortened.)
The calculations needed to obtain the cost of expediting the remaining activities
are shown in Exhibit 5.11A.
3. Compute the critical path. For the simple network we have been using, this
schedule would take 10 days. The critical path is A–B–D.
4. Shorten the critical path at the least cost. The easiest way to proceed is to start
with the normal schedule, find the critical path, and reduce the path time by one
day using the lowest-cost activity. Then recompute and find the new critical path