1. Assignment Problems Variation of transportation problems. One-to-one assignment. Workforce assignments, machine assignments, etc. (go to example)

2. 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

3. 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.

4. Critical Path Method - Terms. Activity on Arc 12 A Nodes: milestones Activity: process 6 Duration (EX: hrs., days)

5. Critical Path Method: Terms “Activity A must be done before B can begin.” - Activity A is a PREDECESSOR of B. 12 A Nodes: milestones 3 B Activities: processes

6. 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 B Activities: processes 4 C

7. 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.

8. 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: 2 6 5 4 6 3 –A: get permits –B: pour foundations –C: frame walls –D: install plumb. –E: install elec. –F: install landscaping –G: move in. Durations: 2 6 5 4 6 9 3

9. 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: 2 6 5 4 6 9 3 Act.Dur.Preds. Post. A2-- D B6-- C,F C5B D D4A,C E E6D G F9B G G3E,F

10. EX: build a house: create CPM Act.Dur.Preds. Post. A2-- D B6-- C,F C5B D D4A,C E E6D G F9B G G3E,F A E D G F C B 6 5 4 6 3 9 2

11. But what is the Critical Path? A E D G F C B 6 5 4 6 3 9 2 The path of activities that takes the longest amount of time; the path with the activities that cannot be altered time-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.