Linear programming and Extensions


Lecture 1 - Introduction to Linear Programming Problems


Lecture 2 - Vector space, Linear independence and dependence, basis


Lecture 3 - Moving from one basic feasible solution to another, optimality criteria


Lecture 4 - Basic feasible solutions, existence & derivation


Lecture 5 - Convex sets, dimension of a polyhedron, Faces, Example of a polytope


Lecture 6 - Direction of a polyhedron, correspondence between bfs and extreme points


Lecture 7 - Representation theorem, LPP solution is a bfs, Assignment 1


Lecture 8 - Development of the Simplex Algorithm, Unboundedness, Simplex Tableau


Lecture 9 - Simplex Tableau & algorithm ,Cycling, Bland’s anti-cycling rules, Phase I & Phase II


Lecture 10 - Big-M method,Graphical solutions, adjacent extreme pts and adjacent bfs


Lecture 11 - Assignment 2, progress of Simplex algorithm on a polytope, bounded variable LPP


Lecture 12 - LPP Bounded variable, Revised Simplex algorithm, Duality theory, weak duality theorem


Lecture 13 - Weak duality theorem, economic interpretation of dual variables, Fundamental theorem of duality


Lecture 14 - Examples of writing the dual, complementary slackness theorem


Lecture 15 - Complementary slackness conditions, Dual Simplex algorithm, Assignment 3


Lecture 16 - Primal-dual algorithm


Lecture 17 - Problem in lecture 16, starting dual feasible solution, Shortest Path Problem


Lecture 18 - Shortest Path Problem, Primal-dual method, example


Lecture 19 - Shortest Path Problem-complexity, interpretation of dual variables, post-optimality analysis-changes in the cost vector


Lecture 20 - Assignment 4, postoptimality analysis, changes in b, adding a new constraint, changes in {aij} , Parametric analysis


Lecture 21 - Parametric LPP-Right hand side vector


Lecture 22 - Parametric cost vector LPP


Lecture 23 - Parametric cost vector LPP, Introduction to Min-cost flow problem


Lecture 24 - Mini-cost flow problem-Transportation problem


Lecture 25 - Transportation problem degeneracy, cycling


Lecture 26 - Sensitivity analysis


Lecture 27 - Sensitivity analysis


Lecture 28 - Bounded variable transportation problem, min-cost flow problem


Lecture 29 - Min-cost flow problem


Lecture 30 - Starting feasible solution, Lexicographic method for preventing cycling ,strongly feasible solution


Lecture 31 - Assignment 6, Shortest path problem, Shortest Path between any two nodes,Detection of negative cycles


Lecture 32 - Min-cost-flow Sensitivity analysis Shortest path problem sensitivity analysis


Lecture 33 - Min-cost flow changes in arc capacities , Max-flow problem, assignment 7


Lecture 34 - Problem 3 (assignment 7), Min-cut Max-flow theorem, Labelling algorithm


Lecture 35 - Max-flow - Critical capacity of an arc, starting solution for min-cost flow problem


Lecture 36 - Improved Max-flow algorithm


Lecture 37 - Critical Path Method (CPM)


Lecture 38 - Programme Evaluation and Review Technique (PERT)


Lecture 39 - Simplex Algorithm is not polynomial time- An example


Lecture 40 - Interior Point Methods