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**The GE Linear Programming & Game Theory Course for Semester III, Delhi University has been taught by Mr. Dheeraj Suri. The Video Lectures are based upon the books prescribed by the University of Delhi. The Duration of Video Lectures is approximately 35 Hours.**

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**Full Course Video Lectures****Complete Study Material (PDF Notes) which includes Concepts, Previous Year Questions, Numerical Questions, MCQ’s and Important Questions****Online Discussion Forum to Post Your Queries to Discuss with Faculty & other fellow Students****Live online Doubts Sessions (at least twice a week) for resolution of Doubts****Mock Tests at the Website****Video Lectures Cover Theory Portions Exchaustively + Complete Solutions of Back Questions of readings + Solutions of Previous Years Papers + Large Number of Numericals**

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**Demo Lectures**

**Demo Lectures****Demo PDF of Study Material**

Chapter-5-Transportation-Problems

**Demo PDF of Study Material****Demo Quiz**

**Exam Pattern**

**The Question Paper of 75 Marks**

**Part**

**Course Content**** of Our ****Video Lectures**

**Course Content****of Our****Video Lectures****Lectures are as per the Latest Syllabus for 2021**

**Lectures are as per the Latest Syllabus for 2021****Unit 1 : ****Linear Programming, Simplex Method & Duality**

**Unit 1 :****Linear Programming, Simplex Method & Duality****Chapter 1 : Introduction to LPP [180 Minutes]**

**Based Upon Thie, Paul R., & Keough, G. E. Chapter 2 & 3**

**Number of Lectures 5 Lectures**

**Total Duration of Lectures 180 Minutes**

**Number of Questions in Notes Questions**

**Number of MCQ Tests on this Chapter Tests**

**Important Topics Covered**

**Introduction to LPP, Formation of LPP, Graphical Method of Solution, Basic Feasible Solution, Unbounded Solution, Multiple Optimal Solutions, Infeasibility, Linear Programming & Convexity**

**Introduction to LPP, Formation of LPP, Graphical Method of Solution, Basic Feasible Solution, Unbounded Solution, Multiple Optimal Solutions, Infeasibility, Linear Programming & Convexity**

**Chapter 2 : Simplex Method [200 Minutes]**

** ****Based Upon Thie, Paul R., & Keough, G. E. Chapter 3**

**Based Upon Thie, Paul R., & Keough, G. E. Chapter 3****Number of Lectures 5 Lectures**

**Total Duration of Lectures 200 Minutes**

**Number of Questions in Notes Questions**

**Number of MCQ Tests on this Chapter Tests**

**Important Topics Covered**

**Simplex Method, Unbounded Solutions, Multiple Optimal Solutions**

**Simplex Method, Unbounded Solutions, Multiple Optimal Solutions****Chapter 3 : Artificial Variables [170 Minutes]**

**Based Upon Thie, Paul R., & Keough, G. E. Chapter 3**

**Number of Lectures 4 Lectures**

**Total Duration of Lectures 170 Minutes**

**Number of Questions in Notes Questions**

**Number of MCQ Tests on this Chapter Tests**

**Important Topics Covered**

**Use of Artificial Variables in Simplex Method, BIG M Method, Infeasibility, Solution of Minimization Problems, **

**Use of Artificial Variables in Simplex Method, BIG M Method, Infeasibility, Solution of Minimization Problems,**

**Chapter 4 : Duality [120 Minutes]**

** ****Based UponThie, Paul R., & Keough, G. E. Chapter 4**

**Based UponThie, Paul R., & Keough, G. E. Chapter 4****Number of Lectures 3 Lectures**

**Total Duration of Lectures 120 Minutes**

**Number of Questions in Notes Questions**

**Number of MCQ Tests on this Chapter Tests**

**Important Topics Covered**

**Meaning of Dual & Primal, Formation of Dual, Interpretation of Dual**

**Meaning of Dual & Primal, Formation of Dual, Interpretation of Dual****Unit 2 : ****Transportation & Assignment Problems**

**Unit 2 :****Transportation & Assignment Problems****Chapter 5 : Transportation Problems [140 Minutes]**

**Based Upon Taha, Hamdy A. Chapter 5**

**Number of Lectures 4 Lectures**

**Total Duration of Lectures 140 Minutes**

**Number of Questions in Notes Questions**

**Number of MCQ Tests on this Chapter Tests**

**Important Topics Covered**

**Introduction to Transportation Problems, Formation of Transportation Problems, Finding Basic Feasible Solution Using : North West Corner Rule, Least Cost Method, Vogel’s Approximation Method; Finding Optimal Solution Using Stepping Stone Method & MODI, Dual of a Transportation Method **

**Introduction to Transportation Problems, Formation of Transportation Problems, Finding Basic Feasible Solution Using : North West Corner Rule, Least Cost Method, Vogel’s Approximation Method; Finding Optimal Solution Using Stepping Stone Method & MODI, Dual of a Transportation Method**

**Chapter 6 : Assignment Problems [100 Minutes]**

** ****Based Upon Taha, Hamdy A. Chapter 5**

**Based Upon Taha, Hamdy A. Chapter 5****Number of Lectures 3 Lectures**

**Total Duration of Lectures 100 Minutes**

**Number of Questions in Notes Questions**

**Number of MCQ Tests on this Chapter Tests**

**Important Topics Covered**

** ****Introduction to Assignment Problems, Formulation of Assignment Problems, Solution of Assignment Problems Using Hungarian Method, Dual of Assignment Problems**

**Introduction to Assignment Problems, Formulation of Assignment Problems, Solution of Assignment Problems Using Hungarian Method, Dual of Assignment Problems****Unit 3 : ****Two Person, Zero Sum Games**

**Unit 3 :****Two Person, Zero Sum Games****Chapter 7 : Introduction to Game Theory [90 Minutes]**

**Based Upon Thie, Paul R., & Keough, G. E. Chapter 9**

**Number of Lectures 2 Lectures**

**Total Duration of Lectures 90 Minutes**

**Number of Questions in Notes Questions**

**Number of MCQ Tests on this Chapter Tests**

**Important Topics Covered**

**Introduction to Game Theory, Formulation of Two Person Zero Sum Rectangular Games, Solution of Rectangular Games with Saddle Points**

**Introduction to Game Theory, Formulation of Two Person Zero Sum Rectangular Games, Solution of Rectangular Games with Saddle Points**

**Chapter 8 : Game Theory Continued [200 Minutes]**

** ****Based Upon Thie, Paul R., & Keough, G. E. Chapter 9**

**Based Upon Thie, Paul R., & Keough, G. E. Chapter 9****Number of Lectures 4 Lectures**

**Total Duration of Lectures 200 Minutes**

**Number of Questions in Notes Questions**

**Number of MCQ Tests on this Chapter Tests**

**Important Topics Covered**

**Mixed Strategies, Dominance Rule, Solution of Games Without Saddle Points, Graphical Solution of Games, Solution of Games Using Simplex Method**

**Mixed Strategies, Dominance Rule, Solution of Games Without Saddle Points, Graphical Solution of Games, Solution of Games Using Simplex Method****End of Syllabus**

**Course Description**

**Course Objective: This course develops the ideas underlying the Simplex method computational techniques for linear programming and game theory, having applications in management, social science, industry, warfare, economics and financial sectors, etc.**

**Course Learning Outcomes: This course will enable the students to learn:**(i) The optimal solution for linear optimization problems subject to certain constraints.

(ii) The dual to a production problem with profits to be maximized to keep total cost down.

(iii) The transportation and Hungarian algorithm specially designed to solve the transportation and assignment problems, respectively.

(iv) The strategies for two-person, zero-sum game are obtained by solving two dual linear programming problems.

**Course Contents :**

**Unit 1. Linear Programming Problem, Simplex Method and Duality**Introduction to Linear Programming Problem: Graphical method of solution, Basic Feasible Solutions, Linear programming and convexity; Introduction to the Simplex method: Theory of the Simplex method, Optimality and unboundedness; The Simplex tableau and examples, Artificial variables; Introduction to Duality, Formulation of the Dual problem with examples and interpretations, The Duality theorem.

**Unit 2. Transportation and Assignment Problems**Definition and mathematical formulation of Transportation problem, Methods of finding initial basic feasible solutions, North West corner rule, Least- cost method, Vogel’s approximation method, Algorithm for solving Transportation problem; Mathematical formulation and Hungarian method of solving Assignment problem.

**Unit 3. Two-Person, Zero-Sum Games**Introduction to Game theory, Formulation of two-person, Zero-sum rectangular game, Solution of rectangular games with saddle points, Mixed strategies, Dominance principle, Rectangular Games without saddle points, Graphical and linear programming solution of rectangular games.

**References:**

- Taha, Hamdy A. (2010). Operations Research: An Introduction (9th ed.). Pearson.
- Thie, Paul R., & Keough, G. E. (2014). An Introduction to Linear Programming and Game Theory. (3rd ed.). Wiley India Pvt. Ltd.