Operations and Supply Chain Management The Core

140 OPERATIONS AND SUPPLY CHAIN MANAGEMENT
Slack time
The time that an
activity can be
delayed without
delaying the
entire project; the
difference between
the late and early
start times of an
activity.
For some activities in a project, there may be some leeway regarding when an activity
can start and finish. This is called the slack time in an activity. For each activity
in the project, we calculate four points in time: the early start, early finish, late
start, and late finish times. The early start and early finish are the earliest times that
the activity can start and be finished. Similarly,
the late start and late finish are the latest times
the activities can start and finish without delaying
the project. The difference between the late
start time and early start time is the slack time.
To help keep all of this straight, we place these
numbers in special places around the nodes that
represent each activity in our network diagram,
as shown here.
Early
start
Late
start
Activity
(duration)
Early
finish
Late
finish
To calculate numbers, start from the beginning of the network and work to the
end, calculating the early start and early finish numbers. Start counting with the
current period, designated as period 0. Activity A has an early start of 0 and an
early finish of 1. Activity B’s early start is A’s early finish or 1. Similarly, C’s early
start is 1. The early finish for B is 3, and the early finish for C is 2. Now consider
activity D. D cannot start until both B and C are done. Because B cannot be done
until 3, D cannot start until that time. The early start for D, therefore, is 3, and the
early finish is 4. Our diagram now looks like this.
1 3
0 1
B(2)
3 4
A(1)
1 2
D(1)
C(1)
To calculate the late finish and late start times, start from the end of the network
and work toward the front. Consider activity D. The earliest that it can be done is
at time 4; and if we do not want to delay the completion of the project, the late finish
needs to be set to 4. With a duration of 1, the latest that D can start is 3. Now
consider activity C. C must be done by time 3 so that D can start, so C’s late finish
time is 3 and its late start time is 2. Notice the difference between the early and late
start and finish times: This activity has one week of slack time. Activity B must be
done by time 3 so that D can start, so its late finish time is 3 and late start time is 1.
There is no slack in B. Finally, activity A must be done so that B and C can start.
Because B must start earlier than C, and A must get done in time for B to start, the
late finish time for A is 1. Finally, the late start time for A is 0. Notice there is no
slack in activities A, B, and D. The final network looks like this. (Hopefully, the
stock your investment team has chosen is a winner!)