Mathematics - Linear programming and Extensions (English)

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Lecture 1: Mod-01 Lec-01 Introduction to Linear Programming Problems.

Lecture 2: Mod-01 Lec-02 Vector space, Linear independence and dependence, basis.

Lecture 3: Mod-01 Lec-03 Moving from one basic feasible solution to another, optimality criteria.

Lecture 4: Mod-01 Lec-04 Basic feasible solutions, existence & derivation.

Lecture 5: Mod-01 Lec-05 Convex sets, dimension of a polyhedron, Faces, Example of a polytope.

Lecture 6: Mod-01 Lec-06 Direction of a polyhedron, correspondence between bfs and extreme points.

Lecture 7: Mod-01 Lec-07 Representation theorem, LPP solution is a bfs, Assignment 1

Lecture 8: Mod-01 Lec-08 Development of the Simplex Algorithm, Unboundedness, Simplex Tableau.

Lecture 9: Mod-01 Lec-09 Simplex Tableau & algorithm ,Cycling, Bland's anti-cycling rules, Phase I & Phase II.

Lecture 10: Mod-01 Lec-10 Big-M method,Graphical solutions, adjacent extreme pts and adjacent bfs

Lecture 11: Mod-01 Lec-11 Assignment 2, progress of Simplex algorithm on a polytope, bounded variable LPP

Lecture 12: Mod-01 Lec-12 LPP Bounded variable, Revised Simplex algorithm, Duality theory, weak duality theorem.

Lecture 13: Mod-01 Lec-13 Weak duality theorem, economic interpretation of dual variables

Lecture 14: Mod-01 Lec-14 Examples of writing the dual, complementary slackness theorem.

Lecture 15: Mod-01 Lec-15 Complementary slackness conditions, Dual Simplex algorithm, Assignment 3.

Lecture 16: Mod-01 Lec-16 Primal-dual algorithm.

Lecture 17: Mod-01 Lec-17 Problem in lecture 16, starting dual feasible solution, Shortest Path Problem.

Lecture 18: Mod-01 Lec-18 Shortest Path Problem, Primal-dual method, example.

Lecture 19: Mod-01 Lec-19 Shortest Path Problem-complexity, interpretation of dual variables

Lecture 20: Mod-01 Lec-20 Assignment 4, postoptimality analysis, changes in b, adding a new constraint

Lecture 21: Mod-01 Lec-21 Parametric LPP-Right hand side vector.

Lecture 22: Mod-01 Lec-22 Parametric cost vector LPP

Lecture 23: Mod-01 Lec-23 Parametric cost vector LPP, Introduction to Min-cost flow problem.

Lecture 24: Mod-01 Lec-24 Mini-cost flow problem-Transportation problem.

Lecture 25: Mod-01 Lec-25 Transportation problem degeneracy, cycling

Lecture 26: Mod-01 Lec-26 Sensitivity analysis

Lecture 27: Mod-01 Lec-27 Sensitivity analysis.

Lecture 28: Mod-01 Lec-28 Bounded variable transportation problem, min-cost flow problem.

Lecture 29: Mod-01 Lec-29 Min-cost flow problem

Lecture 30: Mod-01 Lec-30 Starting feasible solution, Lexicographic method for preventing cycling

Lecture 31: Mod-01 Lec-31 Assignment 6, Shortest path problem, Shortest Path between any two nodes

Lecture 32: Mod-01 Lec-32 Min-cost-flow Sensitivity analysis Shortest path problem sensitivity analysis.

Lecture 33: Mod-01 Lec-33 Min-cost flow changes in arc capacities , Max-flow problem, assignment 7

Lecture 34: Mod-01 Lec-34 Problem 3 (assignment 7), Min-cut Max-flow theorem, Labelling algorithm.

Lecture 35: Mod-01 Lec-35 Max-flow - Critical capacity of an arc, starting solution for min-cost flow problem.

Lecture 36: Mod-01 Lec-36 Improved Max-flow algorithm.

Lecture 37: Mod-01 Lec-37 Critical Path Method (CPM)

Lecture 38: Mod-01 Lec-38 Programme Evaluation and Review Technique (PERT).

Lecture 39: Mod-01 Lec-39 Simplex Algorithm is not polynomial time- An example.

Lecture 40: Mod-01 Lec-40 Interior Point Methods