LECTURE 7: ROBUST LINEAR OPTIMIZATION

15
LECTURE 7: ROBUST LINEAR OPTIMIZATION 1. Motivation 2. Robust model 3. Solution methods

Transcript of LECTURE 7: ROBUST LINEAR OPTIMIZATION

Page 1: LECTURE 7: ROBUST LINEAR OPTIMIZATION

LECTURE 7: ROBUST LINEAR OPTIMIZATION1. Motivation2. Robust model3. Solution methods

Page 2: LECTURE 7: ROBUST LINEAR OPTIMIZATION

Motivation• Example: Pharmaceutic decision making

(from Prof. Tom Luo)

Page 3: LECTURE 7: ROBUST LINEAR OPTIMIZATION

Data sheet

Page 4: LECTURE 7: ROBUST LINEAR OPTIMIZATION

LP formulation

Page 5: LECTURE 7: ROBUST LINEAR OPTIMIZATION

Situation analysis

Page 6: LECTURE 7: ROBUST LINEAR OPTIMIZATION

Robust LP model

Page 7: LECTURE 7: ROBUST LINEAR OPTIMIZATION

Simple form robust LP• Define

• Consider

Page 8: LECTURE 7: ROBUST LINEAR OPTIMIZATION

Assumptions in decision making

Page 9: LECTURE 7: ROBUST LINEAR OPTIMIZATION

Mathematics involved

Page 10: LECTURE 7: ROBUST LINEAR OPTIMIZATION

Semi-infinite LP

Page 11: LECTURE 7: ROBUST LINEAR OPTIMIZATION

Properties of (RLP)sI

Page 12: LECTURE 7: ROBUST LINEAR OPTIMIZATION

Solution method 1

• Pros: Solved by LP• Cons: An approximation solution

Page 13: LECTURE 7: ROBUST LINEAR OPTIMIZATION

Solution method 2

• Consider

Page 14: LECTURE 7: ROBUST LINEAR OPTIMIZATION

Solution method 2

Page 15: LECTURE 7: ROBUST LINEAR OPTIMIZATION

Computational bottleneck