Post on 18-Dec-2015
Assignment Problems
• Variation of transportation problems.
• One-to-one assignment.
• Workforce assignments, machine assignments, etc.
• (go to example)
Project Modeling: CPM
• How to organize? How to plan?
• How long will the entire project take?
• Critical Path Model - Terms– Activity on Arc– predecessor– duration
Project Modeling: CPM
• How to organize? How to plan?
• How long will the entire project take?
• Critical Path Model - Terms– Activity on Arc– predecessor– duration
As long as the longest (duration) series of activities takes -- also call the CRITICAL PATH.
Critical Path Method - Terms.• Activity on Arc
1 2A
Nodes: milestones
Activity: process
6
Duration (EX: hrs., days)
Critical Path Method: Terms• “Activity A must be done before B can
begin.” - Activity A is a PREDECESSOR of B.
1 2A
Nodes: milestones
3B
Activities: processes
Critical Path Method: Terms• “Activities A and B must be done before C
can begin.” - A & B are PREDECESSORS of C.
1
2
A
Nodes: milestones
3
BActivities: processes
4C
EX: build a house: the tasks (activities) in order
– get permits– pour foundations– frame walls – install plumbing systems– install electrical systems– install landscaping– move in.
EX: build a house: add durations and label activities
– A: get permits– B: pour foundations– C: frame walls – D: install plumbing– E: install electrical – F: install landscaping– G: move in.
Durations:26
5
46
3
– A: get permits– B: pour foundations– C: frame walls – D: install plumb.– E: install elec.– F: install landscaping – G: move in.
Durations:26
5
46
9
3
EX: build a house: create table– A: get permits– B: pour foundations– C: frame walls – D: install plumb.– E: install elec.– F: install landscaping – G: move in.
Durations:26
5
46
9
3
Act. Dur. Preds. Post.A 2 -- DB 6 -- C,FC 5 B DD 4 A,C EE 6 D GF 9 B GG 3 E,F
EX: build a house: create CPMAct. Dur. Preds. Post.A 2 -- DB 6 -- C,FC 5 B DD 4 A,C EE 6 D GF 9 B GG 3 E,F
AED
G
FC
B6
5
4 63
9
2
But what is the Critical Path?
AED
G
FC
B6
5
4 63
9
2
The path of activities that takes the longest amount oftime; the path with the activities that cannot be alteredtime-wise without changing the overall project duration.
(We need to tell the family when they will be settled in their new house -- how soon?)
Use Excel to set up this problem and find the critical path.