IE310. Operations ResearchChapter 6. Duality Theory and Sensitivity AnalysisLecture 11 Duality Theory (2)Ruoyu SunISE Department1
2Review Questions of Lecture 11•What is a dual problem of a standard LP?How to interpret the dual problem, using Burger/Pizza restaurant as anexample?•How to interpret the dual problem of the primal problem, using Ford/Tesla asan example?•How to interpret the dual problem, using Burger/Pizza restaurant as anexample?y
3This Lecture•Duality theory: weak duality and strong dualityAfter today’s lecture, you should be able to•Describe the relation between primal and dual LP•Find a complementary basic solution for a given primal BF solution
4Homework 3 correction•homework#3, question 4.6-5, part (b) asks to use acomputer packagebasedon the simplex method to determine that the problem has no feasible solution.•Skip this part.•You still need to answer other parts, (a), (c), (d).
5Question on Software•Will we learn software? Very very briefly later; not in detail.•Benefit of understanding the procedure of simplex method (by hand):•1) More interpretable.--Counter-example: blackbox: deep learninge.g. after reading images and descriptions of symptoms, the computergenerates output: this patient has gotappendicitis. But the patient may or maynot believe the computer’s output.--OR methods, like LP are often much more interpretable•E.g. If you just run software to solve how to assign the numbers ofburgers/pizzas to produce, and make recommendation to your boss. Yourboss may not believe you•You can tell your boss: let me show you a toy example, run 2 iterations ofsimplex method to get the solution. Explain each step.•2) another benefit: debug. On GANs, quite hard to debug; for LP, you knowmuch better how to debug•3) post-optimality analysis
6BasicVarZOriginal VariablesSlack VariablesRHSZ1cBTB-1A–cT= yTA-cTcBTB-1=yTcBTxB=cBTB-1b=yTbxB0B-1AB-1xB=B-1bItsdual LP:minbTys.t.ATy≥cy≥0Relation of Dual LP and Simplex Tableau?Simplex Tableau of the standard form