This document discusses time-cost tradeoffs in project management. It defines key terms like normal activity time, crash activity time, direct costs, and indirect costs. It explains that direct costs generally increase as activity times decrease, while indirect costs decrease as the overall project duration decreases. The optimal project duration is the point of minimum total cost, found by balancing increased direct costs from crashing activities against decreased indirect costs from a shorter schedule. The document provides an example of calculating time-cost tradeoffs for activities on a project's critical path.

1. Time-Cost Trade offs
FPE 444: ENGINEERING
PROJECT MANAGEMENT
LECTURE EIGHT

2. Project Crashing and Time-Cost Trade-Off
General Relationship of Time and Cost
The time-cost trade-off
2

3. Project Crashing and Time-Cost Trade-Off
General Relationship of Time and Cost
■ Project crashing costs and indirect costs have an
inverse relationship.
■ Crashing costs are highest when the project is
shortened.
■ Indirect costs increase as the project duration
increases.
■ The optimal project time is at the minimum point on
the total cost curve.
3

4. The main purpose of this lecture is to
demonstrate a procedure to determine activity
schedules to reduce the project duration time
with a minimum increase in the project
direct costs, by buying time along the
critical path (s) where it can be obtained at
least cost.
Purpose of Time Reduction Technique
Assumption: It is assumed in all of the procedures that are presented in
this topic that unlimited resources are available.

5.  The results of planning and scheduling stages of
the critical path method provide a network plan for
the activities making up the project and a set of
earliest and latest start and finish times for each
activity.
 In particular, the earliest occurrence time for the
network terminal event is the estimated “normal”
project duration time, based on “normal” activity
time estimates.
Time-Cost Trade-off

6.  To meet the customer contractually required time.
 To recover time of delays, that occur in the early stages
of the project, to avoid paying liquated damages, or
avoid damaging the company relationship with the
customer.
 To complete a project earlier than schedule in order to
free resources used and move on to another project.
 To avoid adverse weather.
 To receive an early-completion bonus.
 To meet a client’s desire for expediting the project.
Why Project Time Reduction

7. Buy Time
 Have the existing crew work overtime.
 Bring in additional workers (resources) up to
practical limit.
 Work on multiple shifts.
 Achieve more output by offering incentive
payments.
 Use better/more advanced equipment(s).
 Use more quickly installed materials.
 Use subcontractors.
 Change construction method.
How to Shorten Project Time

8. Definitions
Activity time-cost trade-off input for the CPM procedure

9. A simple representation of the possible relationship between the duration of an activity
and its direct costs appears in Figure below. Considering only this activity in isolation
and without reference to the project completion deadline, a manager would choose a
duration which implies minimum direct cost, called the normal duration. At the other
extreme, a manager might choose to complete the activity in the minimum possible
time, called crashed duration, but at a maximum cost.

10. The linear relationship shown above between these two points
implies that any intermediate duration could also be chosen. It
is possible that some intermediate point may represent the
ideal or optimal trade-off between time and cost for this activity.
The slope of the line connecting the normal point (lower point)
and the crash point (upper point) is called the cost slope of the
activity. The slope of this line can be calculated mathematically
by knowing the coordinates of the normal and crash points.

11. 1. Activity Direct Cost: It includes the cost of the
material, equipment, and direct labor required
to perform the activity in question. If the activity
is entirely performed by a subcontractor, then
the activity direct cost is equal to the price of
the subcontract, plus any added fees.
2. Project indirect cost: It includes, supervision
and other overhead costs, interest charges on
project investment, penalty costs due to poor
quality or delayed projects.
Definitions

12. 3. Normal Activity Time: It is the normal time
that is used in the basic critical path planning
and scheduling based on the normal
level of resource.
4. Normal Activity Cost: The normal activity
cost is equal to the minimum of direct costs
required to perform the activity, and the
corresponding activity duration is called
the normal time.
Definitions

13. 5. Crash Activity Time: Minimum
activity duration time that is technically
possible.
6. Crash Cost: is assumed to be the
minimum direct cost required to
achieve the crash performance time.
Definitions

14.  The relationship between the activity
direct cost and activity time may be
straight line, continuous curve, or point.
 The direct cost tends to increase if
less time is available for activity.
 Time reduction approach assumed here
will be based on simple linear time-
cost trade-off for each activity.
Activity Direct Cost / Time Relationship

15.  The indirect cost tends to increase if
more time is consumed for the project.
 The indirect cost is generally vary
approximately linearly with the time.
Indirect Cost / Time Relationship

16. Total project costs include both direct costs and
indirect costs of performing the activities of the project.
Direct costs for the project include the costs of
materials, labor, equipment, and subcontractors.
Indirect costs, on the other hand, are the necessary
costs of doing work which can not be related to a
particular activity, and in some cases can not be
related to a specific project.
If each activity was scheduled for the duration that
resulted in the minimum direct cost in this way, the
time to complete the entire project might be too long
and substantial penalties associated with the late
project completion might be incurred.

17. Optimum Contract Duration
Optimum contract duration = project
schedule for minimum total cost

18. Thus, planners perform what is called time-cost trade-
off analysis to shorten the project duration. This
can be done by selecting some activities on the critical
path to shorten their duration.
As the direct cost for the project equals the sum of the
direct costs of its activities, then the project direct cost
will increase by decreasing its duration.
On the other hand, the indirect cost will decrease by
decreasing the project duration, as the indirect cost
are almost a linear function with the project duration.

19. The project total time-cost relationship can be determined by
adding up the direct cost and indirect cost values together as
shown. The optimum project duration can be determined as
the project duration that results in the least project total cost.

20. Example
The durations and direct costs for each activity
in the network of a small construction contract
under both normal and crash conditions are
given in the following table.
a) Establish the least cost for expediting the
contract.
b) Determine the optimum duration of the
contract assuming the indirect cost is 125€
/day.

22. The cost slope of each activity is calculated. Both the
crashability and the cost slope are shown beneath
each activity in the precedence diagram. The critical
path is A-C-G-I and the contract duration in 59 days.