IE-513 Linear Programming

Prof. Barbaros Tansel

2010-2011- Spring

Theory, algorithms, and computational aspects of linear programming. Formulation of problems as linear programs. Development of simplex algorithm, geometry of simplex method, duality theory, and economic interpretations. Sensitivity analysis. Variants of simplex method..

 Lecture 41 (2011-05-11)
Network simplex method for lower and upper bounded minimum cost network flow problems
 
 Lecture 40 (2011-05-09)
Minimum cost network flows (cont'd)
 
 Lecture 39 (2011-05-09)
Minimum cost network flows (cont'd)
 
 Lecture 38 (2011-05-04)
Introduction to minimum cost network flow problems
 
 Lecture 37 (2011-05-02)
Decomposition (cont'd)
 
 Lecture 36 (2011-05-02)
Decomposition (cont'd)
 
 Lecture 35 (2011-04-27)
Parametric right hand sides and decomposition
 
 Lecture 34 (2011-04-25)
Range analysis and parametric costs
 
 Lecture 33 (2011-04-25)
Sensitivity analysis
 
 Lecture 32 (2011-04-20)
Dual simplex method
 
 Lecture 31 (2011-04-18)
Example and economical interpretation
 
 Lecture 30 (2011-04-18)
Duality theorems
 
 Lecture 29 (2011-04-06)
Duality (cont'd)
 
 Lecture 28 (2011-04-04)
Simplex for bounded variables and duality
 
 Lecture 27 (2011-04-04)
Simplex for bounded variables
 
 Lecture 26 (2011-03-30)
Revised simplex and simplex for bounded variables
 
 Lecture 25 (2011-03-28)
Revised Simplex method
 
 Lecture 24 (2011-03-28)
Degeneracy and resolution of cycling
 
 Lecture 23 (2011-03-23)
2-Phase Method to find an initiating basic feasible solution
 
 Lecture 22 (2011-03-21)
Finding a starting basic feasible solution
 
 Lecture 21 (2011-03-21)
Simplex tableau in matrix form, alternative optima, unbounded solution
 
 Lecture 20 (2011-03-16)
Simplex Method in matrix form
 
 Lecture 19 (2011-03-14)
Simplex method explained in terms of basis matrices
 
 Lecture 18 (2011-03-14)
Simplex method example in dictionary form, equation form and tabular form
 
 Lecture 17 (2011-03-07)
Optimality of extreme points and unboundedness, simplex method example
 
 Lecture 16 (2011-03-07)
Directions and unbounded LPs, extreme directions, representation theorem
 
 Lecture 15 (2011-03-02)
Adjacent basic solutions, degeneracy, existence of extreme points, rays, directions of convex sets.
 
 Lecture 14 (2011-02-28)
Adjacent basic solutions, polyhedra in standard form and basic solutions for standard form.
 
 Lecture 13 (2011-02-28)
Equivalence of basic feasible solutions, extreme points and vertices
 
 Lecture 12 (2011-02-23)
Extreme points of polyhedra, basic and basic feasible solutions
 
 Lecture 11 (2011-02-21)
Subspaces, affine subspaces
 
 Lecture 10 (2011-02-21)
Convex hulls, extreme points, vertices
 
 Lecture 9 (2011-02-16)
Convexity, hyperplanes, half-spaces.
 
 Lecture 8 (2011-02-14)
Convex sets and convex functions
 
 Lecture 7 (2011-02-14)
Fourier-Motzkin elimination to solve linear inequality systems
 
 Lecture 6 (2011-02-09)
Conversions of constraints and variables. Requirements space
 
 Lecture 5 (2011-02-07)
Examples of linear programming formulation (cont
 
 Lecture 4 (2011-02-07)
Examples of linear programming formulation
 
 Lecture 3 (2011-02-02)
General form linear programming and matrix forms, two formulation examples
 
 Lecture 2 (2011-01-31)
Example continued with solution and general form of linear programming in canonical maximization form
 
 Lecture 1 (2011-01-31)
Brief history of linear programming and introductory example
 

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