 # Linear Programming Teacher

##### Dr. Mohammed Siddique Category

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# Code(Credit) : CUTM1523 (3-2-1)

## Course Objectives

• To introduce a brief understanding about Linear Programming Problems.
• To cater the characteristics of Linear Programming Problems and its Applications.
• To demonstration of the utilization of Linear Programming Problems in industry and business.

## Learning Outcomes

Upon successful completion of this course, students will be able to:

• Formulate the necessary and sufficient optimality conditions for linear programming and demonstrate the geometrical interpretation of these conditions.
• Use various techniques to solve basic transportation and network problems.
• Use the mathematical foundations learned in this course to formulate new applications as optimal decision problems and seek appropriate solutions algorithms.

## Course Syllabus

Module I (5 Hours)

Linear programming problems (LPP): Introduction to linear programming problems (LPP), Mathematical formulation of the linear programming problems with illustrations

Practice 1: (2 Hours)

Formulation of maximization type linear programming problem using excel solver

Practice 2: (2 Hours)

Formulation of minimization type linear programming problem using excel solver

Assignment 1: (2 Hours)

Formulation of Manufacturing/Production Problem to LPP

Module II (4 Hours)

Graphical method used for solving linear programming problem. Feasible region of LPP, unbounded solution to the LPP in graphical method, Canonical and standard form of LPP.

Practice 3: (2 Hours)

Solution of graphical method of LPP using excel solver

Practice 4: (2 Hours)

Solving manufacturing problem using excel solver

Practice 5: (2 Hours)

Solving diet problem using in excel solver

Assignment 2: (2 Hours)

Formulation of investment and diet problems to LPP and its graphical solution.

Module III (5 Hours)

Simplex Method: Basic and non basic variables, Theory of Simplex method, optimality and unboundlessness, Simplex algorithm, Simplex method in tableau format.

Practice 6: (2 Hours)

Solving Maximization problem using Simplex method in excel solver

Practice 7: (2 Hours)

Solving Minimization problem using Simplex method in excel solver

Assignment 3: (2 Hours)

Solution of linear programming problem using simplex method.

Module IV: (5 Hours)

Introduction to artificial variables, Two –phase simplex method, Big-M method, Degeneracy problem in simplex method

Practice 8: (2 Hours)

Solving linear-programming problem using Two Phase method in excel solver

Practice 9: (2 Hours)

Solving linear-programming problem using Big-M method in excel solver

Assignment 4: (2 Hours)

Solution of linear programming problem using penalty method.

Module V: (4 Hours)

Transportation Problem: Introduction to transportation problem, Initial basic feasible solution to transportation problem using North-West Corner, Least Cost Method and Vogel's approximation Method.

Practice 10: (2 Hours)

Solving Transportation problem using North West Corner method in excel solver

Practice 11: (2 Hours)

Solving Transportation problem using Least Cost method in excel solver

Assignment 5:

Initial basic feasible solution to transportation problem

Module VI: (4 Hours)

Optimal solution to transportation problem using MODI method, Unbalanced transportation problem, Degeneracy in transportation problem.

Practice 12: (2 Hours)

Solving Transportation problem using Vogel's Approximation method in excel solver

Assignment 6: (2 Hours)

Optimal solution to transportation problem using MODI method

Module VII: ( 4 Hours)

Assignment Problem: Introduction to assignment problem, Mathematical formulation of assignment problem, Solution to assignment problem using Hungarian method

Assignment 7: (2 Hours)

Solution to assignment problem using Hungarian method

Text Books:

1. Kanti Swarup, P.K. Gupta and Man Mohan-Operations Research, S. Chand and Co. Pvt.Ltd.
2. Kalavathy- Operations Research, Vikas Publishing House Pvt. Ltd.

Reference Book:

1. Mathematical Programming by N. S. Kambo, East West Press.

## Session 2 & 3

Mathematical formulation of production problem to the linear programming problem

## Session 4

Mathematical formulation of diet problem to the linear programming problem

## Session 5

Mathematical formulation of investment  problem to the linear programming problem

## Practice 1

Formulation of maximization type linear programming problem using excel solver

## Practice 2

Formulation of minimization type linear programming problem using excel solver

## Assignment 1

Formulation of Manufacturing/Production Problem to LPP

## Session 12

Procedure for solving linear programming problems by Graphical method

## Session 13 & 14

Solving linear programming problems by graphical method

## Practice 3

Solution of graphical method of LPP using excel solver

## Practice 4

Solving manufacturing problem using in excel solver

## Practice 5

Solving diet problem using excel solver

## Assignment 2

Formulation of investment and diet problems to LPP and its graphical solution

## Practice 6

Solving Maximization problem using Simplex method in excel solver

## Practice 7

Solving Minimization problem using Simplex method in excel solver

## Assignment 3

Solution of linear programming problem using simplex method

## Practice 8

Solving linear-programming problem using Two Phase method in excel solver

## Practice 9

Solving linear-programming problem using Big-M method in excel solver

## Assignment 4

Solution of linear programming problem using penalty method

## Session 49

Initial basic feasible solution to transportation problem using Vogel's approximation Method

## Practice 10

Solving Transportation problem using North West Corner method in excel solver

## Practice 11

Solving Transportation problem using Least Cost method in excel solver

## Assignment 5

Initial basic feasible solution to transportation problem

## Practice 12

Solving Transportation problem using Vogel's Approximation method in excel solver

## Assignment 6

Optimal solution to transportation problem using MODI method

## Assignment 7

Solution to assignment problem using Hungarian method 