1. Chapter 5: Project Time Management Doddy Prayogo, Ph.D.

2. Shortest Path Problem Eye-ball Solution: Optimal (1,3,4,5,7,9)
Second best
(1,2,4,5,7,9)

3. Longest Path Problem
Set F(9)=0
Set G(1)=0

4. CPM Project Scheduling Tool Longest path problem
Precedence relationships
Activity-on-Arrow
Activity-on-Node B D 3 B D A
Fin A 1 2 4 C C

5. 2 Versions of Network Diagrams
Activity-on-Arrow (AOA) networks
also called Arrow Diagramming Method (ADM)
simpler for projects with many dependencies
emphasizes events; milestones can be easily flagged
sometimes requires dummy activities
Activity-on-Node (AON) networks
also called Precedence Diagramming Method (PDM)
easier to draw for simple projects
emphasizes activities
no dummy activities
Part 5 - Project Scheduling

6. Renovation Project

7. In Network

8. Tree of Longest Path Earliest start times
The project takes at least 26 weeks
It takes 11 weeks to start activity f, which is the sum of lengths of activities a and c

9. Critical Path
A sequence of activities that cannot be delayed without increasing the completion time
S-a-c-e-j-F

10. Tree of Longest Path
Latest finish times

11. Maximum delay = Total float

12. Objective Why don’t we just minimize ESfin?
This cannot force each task to start as earliest as possible, which is usually required in practice to save some floats for emergency

13. Crashing Allocate extra budget can often shorten the project duration
Two classes of problem:
Deadline problem: how to minimize the total cost while meeting a pre-specified deadline
Budget problem: how to minimize the project duration without exceeding budget