**# playlist of the 40 videos (click the up-left corner of the video)**

source: nptelhrd 2012年1月29日

Mathematics - Linear programming and Extensions by Prof. Prabha Sharma, Department of Mathematics and Statistics, IIT Kanpur. For more details on NPTEL visit http://nptel.iitm.ac.in

01 Introduction to Linear Programming Problems. 49:17

02 Vector space, Linear independence and dependence, basis. 58:32

03 Moving from one basic feasible solution to another, optimality criteria. 1:02:38

04 Basic feasible solutions, existence & derivation. 1:00:46

05 Convex sets, dimension of a polyhedron, Faces, Example of a polytope. 1:00:30

06 Direction of a polyhedron, correspondence between bfs and extreme points. 48:09

07 Representation theorem, LPP solution is a bfs, Assignment 1 59:32

08 Development of the Simplex Algorithm, Unboundedness, Simplex Tableau. 56:52

09 Simplex Tableau & algorithm ,Cycling, Bland's anti-cycling rules, Phase I & Phase II. 1:01:07

10 Big-M method,Graphical solutions, adjacent extreme pts and adjacent bfs 59:01

11 Assignment 2, progress of Simplex algorithm on a polytope, bounded variable LPP 1:02:26

12 LPP Bounded variable, Revised Simplex algorithm, Duality theory, weak duality theorem. 53:43

13 Weak duality theorem, economic interpretation of dual variables 57:17

14 Examples of writing the dual, complementary slackness theorem. 53:56

15 Complementary slackness conditions, Dual Simplex algorithm, Assignment 3. 50:38

16 Primal-dual algorithm. 59:46

17 Problem in lecture 16, starting dual feasible solution, Shortest Path Problem. 56:30

18 Shortest Path Problem, Primal-dual method, example. 57:38

19 Shortest Path Problem-complexity, interpretation of dual variables 51:56

20 Assignment 4, postoptimality analysis, changes in b, adding a new constraint 56:11

21 Parametric LPP-Right hand side vector. 52:30

22 Parametric cost vector LPP 59:08

23 Parametric cost vector LPP, Introduction to Min-cost flow problem. 47:52

24 Mini-cost flow problem-Transportation problem. 56:28

25 Transportation problem degeneracy, cycling 1:06:19

26 Sensitivity analysis 1:00:21

27 Sensitivity analysis. 54:53

28 Bounded variable transportation problem, min-cost flow problem. 58:55

29 Min-cost flow problem 58:19

30 Starting feasible solution, Lexicographic method for preventing cycling 59:23

31 Assignment 6, Shortest path problem, Shortest Path between any two nodes 55:04

32 Min-cost-flow Sensitivity analysis Shortest path problem sensitivity analysis. 49:41

33 Min-cost flow changes in arc capacities , Max-flow problem, assignment 7 55:43

34 Problem 3 (assignment 7), Min-cut Max-flow theorem, Labelling algorithm. 1:01:26

35 Max-flow - Critical capacity of an arc, starting solution for min-cost flow problem. 1:04:06

36 Improved Max-flow algorithm. 56:54

37 Critical Path Method (CPM) 55:40

38 Programme Evaluation and Review Technique (PERT). 45:42

39 Simplex Algorithm is not polynomial time- An example. 58:42

40 Interior Point Methods 53:48

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