1. Project Management Planning Models
CPM Method
Time-Cost Model
Compiled by:
Alex J. Ruiz-Torres, Ph.D.
From information developed by many.

2. CPM Method A project is made up of a set of activities.
Activities have dependencies, therefore a project is a network of activities.
The path (s) taking longest time through this network of activities is called the “critical path”
Critical Path Method (CPM) helps to identify the critical activity sequence.
PMr must specially monitor activities in the critical path as any delays in those activities will delay the project.

3. CPM Method Example project. Outcome: prototype design
It has the following five activities:
Define customer requirements (1 week)
Develop software requirements (4 weeks)
Develop hardware requirements (3 weeks)
Develop energy models (5 weeks)
Complete design module (2 weeks)
What is the project’s completion time?

4. CPM Method
The process
List all the activities per order of precedence, starting with the activities that have no precedence.
Create a diagram of all the activities, connecting those that have a precedence constraint. Point the arrow in the direction of time (the next step).

5. CPM Method
Calculate a Early Start (ES) and Early Finish (EF) time for each activity. ES is earliest time that an activity can start given its precedence activities, therefore the EF of the predecessors. If an activity has two or more predecessors, the largest EF of the predecessors is the ES of the activity. EF = ES + activity time.
For the last activity, the Late Start (LS) and the Late Finish (LF) are the same as the Early Start and the Early Finish respectively.

6. CPM Method
Move the LS from the activity to all the predecessors’ LF. If the activity is a predecessor to more than one activity, select the smallest LS. LS = LF - activity time.
Repeat step 6 until all activities have a LS and LF.
Calculate the slack (S) of each activity. S = LS – ES.
Activities with a slack of 0 are in the critical path. Note that it is possible to have multiple critical paths.

7. CPM Method An Example Activity Code Time Pred. R & D R 11 -
Beta Development B 3
Hardware Req. H 5
Testing T 7
Analysis Mechanical M
H. T
Analysis Electrical E 4
H, T
Documentation Write up D
M, E

8. B T M D R H E Activity Code Time Pred. R & D R 11 - Beta Development B3
Hardware Req. H 5
Testing T 7
Analysis Mechanical M
H. T
Analysis Electrical E 4
H, T
Documentation Write up D
M, E
14 | 21
11 | 14
21 | 28 B T M D R
28 | 31 H E
0 | 11
11 | 16
16 | 21
21 | 25
24 | 28

9. Time Cost Model
Project Management process that considers the tradeoffs between the time to complete a project and its cost.
Requires additional information for each task.
Regular time and cost: the duration of the task at its normal pace and the associated cost.
Crash time and cost: the duration of the task if its was performed as fast as possible and the associated cost.

10. Time Cost Model For example Activity: develop software interface.
Regular time and cost: 3 weeks, $6,000
Crash time and cost: 1 week, $9,000
Increase in cost assumes having to pay overtime and premium rates for resources.
The model assumes the activity could be performed in
3 weeks at $6,000 (regular)
2 weeks at $7,500 (partially crashed)
1 week at $9,000 (fully crashed)

11. Time Cost Model Process for Time-Cost Model
Develop the network. Determine the CP, completion time and cost of the project based on the normal estimates.
Determine the crashing rate ($ per time unit) for each task. = (CC-NC)/(CT-NT).
Select an activity in the CP to crash by the lowest possible cost. If no activity in the CP can be crashed the process ends.
Crash that activity by one time unit.
Determine the CP, completion time and cost of the project based on the revised times/cost.
Return to step 3.

12. Time Cost Model
The process results in multiple project plans, each with a CP, completion time, and total cost.
The result is a tradeoff set of project plans.
For example:
At the total crash, the project will take 10 weeks and cost $52,000
$50K
Management must decide what is the best plan based on its customers, budgets, etc.
At the normal time the project will take 17 weeks and cost $20,000
$35K
Cost
$20K
weeks
Completion Time