Learn · Linear programming and Extensions
Lecture 9 of 40Linear programming and Extensions
Lecture_9_ Simplex Tableau & algorithm ,Cycling, Bland’s anti-cycling rules, Phase I & Phase II.
Prof. Prabha Sharma · IIT Kanpur
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All the lectures
- Lecture_01_Introduction to Linear Programming Problems.
- Lecture_02_ Vector space, Linear independence and dependence, basis.
- Lec_03_Moving from one basic feasible solution to another, optimality criteria.
- Lecture_04_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_08_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 .