Optimization Techniques - W2023 - Lecture 4 (Integer Linear Programming & Sensitivity Analysis)

The course "Optimization Techniques" (ENGG*6140, section 2) at the School of Engineering at the University of Guelph. Instructor: Benyamin Ghojogh
Lecture 4 continues the tableau method (simplex algorithm) for linear programming and then explains the branch and bound method for solving integer linear programming. Afterwards, sensitivity analysis in linear programming is introduced.

Chapters:

0:00 - Answering questions about assignment
12:20 - Infeasibility in big M method
15:24 - The reason for the tableau method
28:10 - Dual problem for minimization in linear programming
46:10 - Dual simplex method
54:45 - Handling greater-than-or-equal-to constraints in linear programming
58:15 - Handling not-necessarily non-negative optimization variables in linear programming
1:00:22 - Dual simplex method for greater-than-or-equal-to constraints in maximization
1:05:17 - Introducing integer linear programming
1:22:08 - The branch and bound method
1:46:53 - Introducing sensitivity analysis in linear programming
1:48:56 - Matrices and vectors in linear programming
2:09:43 - Cases for sensitivity analysis
2:12:18 - Case 1-1 (coefficient change of nonbasic variable in objective function)
2:22:07 - Case 1-2 (coefficient change of basic variable in objective function)
2:28:08 - Case 2-1 (coefficient change of nonbasic variable in constraints)
2:32:28 - Case 2-2 (coefficient change of basic variable in constraints)
2:34:50 - Talking about next sessions
2:36:53 - When to use the table formula in the tableau method
2:38:23 - Talking about midterm

[mohammadrashedi]

Thanks for sharing the slides. I think the slides 46 and 47 can be described in a better way by saying that variables y1 and y2 are two new variables (dual variables). Based on these variables, we intentionally want to create that three-fold inequality so that we find the cost function to be maximized. That was a bit unclear how that three-fold inequality came from!