Linear Programming

Teacher

Dr. Mohammed Siddique

Category

Core Courses

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Course Name : Linear Programming

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

https://www.youtube.com/watch?v=oaEmCiKMmdI

 

https://www.youtube.com/watch?v=TwAvQJAM9Hk

Session 4

Mathematical formulation of diet problem to the linear programming problem

 

https://www.youtube.com/watch?v=dfC9rDco0yU&list=PLgA4wLGrqI-ll9OSJmR5nU4lV4_aNTgKx&index=12 

Session 5

Mathematical formulation of investment  problem to the linear programming problem

https://www.youtube.com/watch?v=-32jcGMpD2Q

Session 6 & 7

Practice 1

Formulation of maximization type linear programming problem using excel solver

https://www.youtube.com/watch?v=rQt_SWrOktg

https://www.youtube.com/watch?v=oaEmCiKMmdI

Session 8 & 9

Practice 2

Formulation of minimization type linear programming problem using excel solver

https://www.youtube.com/watch?v=hv6PUL9tiTs

Session 10 & 11

Assignment 1

Formulation of Manufacturing/Production Problem to LPP

Session 12

Procedure for solving linear programming problems by Graphical method

https://www.youtube.com/watch?v=po06JU0c8ME&list=PLgA4wLGrqI-ll9OSJmR5nU4lV4_aNTgKx&index=6

Session 13 & 14

Solving linear programming problems by graphical method

https://www.youtube.com/watch?v=O6QO3J_85as

https://www.youtube.com/watch?v=gbL3vYq3cPk

Session 16 & 17

Practice 3

Solution of graphical method of LPP using excel solver

https://www.youtube.com/watch?v=pQp4GZfoxTo

https://www.youtube.com/watch?v=aAcZPU6l4As

Session 18 & 19

Practice 4

Solving manufacturing problem using in excel solver

https://www.youtube.com/watch?v=tJkHxpoX3kU

Session 20 & 21

Practice 5

Solving diet problem using excel solver

https://www.youtube.com/watch?v=870UDhR9sVo&t=15s

Session 22 & 23

Assignment 2

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

Session 27 & 28

Session 29 & 30

Practice 6

Solving Maximization problem using Simplex method in excel solver

https://www.youtube.com/watch?v=LSEnzps3NVQ

Session 31 & 32

Practice 7

Solving Minimization problem using Simplex method in excel solver

https://www.youtube.com/watch?v=6xa1x_Iqjzg&t=743s

Session 33 & 34

Assignment 3

Solution of linear programming problem using simplex method

Session 40 & 41

Practice 8

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

https://www.youtube.com/watch?v=6xa1x_Iqjzg&t=646s

Session 42 & 43

Practice 9

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

https://www.youtube.com/watch?v=Odmx3CBcdz8

Session 44 & 45

Assignment 4

Solution of linear programming problem using penalty method

Session 47

Session 48

Session 49

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

https://www.youtube.com/watch?v=6MB4ns6Evak&list=PLgA4wLGrqI-ll9OSJmR5nU4lV4_aNTgKx&index=30

https://www.youtube.com/watch?v=ip6Hu_jmMeY

Session 50 & 51

Practice 10

Solving Transportation problem using North West Corner method in excel solver

https://www.youtube.com/watch?v=qjM_5RP-eJw

Session 52 & 53

Practice 11

Solving Transportation problem using Least Cost method in excel solver

https://www.youtube.com/watch?v=DBGbUE6GMIc

Session 54 & 55

Assignment 5

Initial basic feasible solution to transportation problem

Session 60 & 61

Practice 12

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

https://www.youtube.com/watch?v=DlVprABPLlY

Session 62 & 63

Assignment 6

Optimal solution to transportation problem using MODI method

Session 65

Session 68 & 69

Assignment 7

Solution to assignment problem using Hungarian method

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    Dr. Mohammed Siddique

    Asst. Prof. Department of Mathematics
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    Dr. Mohammed Siddique, received Ph. D in Mathematics in the area of Optimization Techniques and Machine Learning from KIIT, Deemed to be University, Bhubaneswar and completed his M.Sc in Mathematics and M.Tech in Computer Science from Utkal University, Bhubaneswar.  He is having more than 16 years of teaching experience. He is having more than 50 […]