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

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

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

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

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

Renovation Project

In Network

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

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

Tree of Longest Path Latest finish times

Maximum delay = Total float

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

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