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.