## PTCCS357 Syllabus - Optimization Techniques - 2023 Regulation Anna University

PTCCS357

OPTIMIZATION TECHNIQUES

L T P C

2 0 2 3

COURSE OBJECTIVES: The objective of this course is to enable the student to
• Formulate and solve linear programming problems (LPP)
• Evaluate Integer Programming Problems, Transportation and Assignment Problems.
• Obtain a solution to network problems using CPM and PERT techniques.
• Able to optimize the function subject to the constraints.
• Identify and solve problems under Markovian queuing models.

UNIT I

LINEAR MODELS

6

Introduction of Operations Research - mathematical formulation of LPP- Graphical Methods to solve LPP- Simplex Method- Two-Phase method

UNIT II

INTEGER PROGRAMMING AND TRANSPORTATION PROBLEMS

6

Integer programming: Branch and bound method- Transportation and Assignment problems - Traveling salesman problem.

UNIT III

PROJECT SCHEDULING

6

Project network -Diagram representation – Floats - Critical path method (CPM) – PERT- Cost considerations in PERT and CPM.

UNIT IV

CLASSICAL OPTIMIZATION THEORY

6

Unconstrained problems – necessary and sufficient conditions - Newton-Raphson method, Constrained problems – equality constraints – inequality constraints - Kuhn-Tucker conditions.

UNIT V

QUEUING MODELS

6

Introduction, Queuing Theory, Operating characteristics of a Queuing system, Constituents of a Queuing system, Service facility, Queue discipline, Single channel models, multiple service channels.

PRACTICALS: 30 PERIODS
1. Solving simplex maximization problems using R programming.
2. Solving simplex minimization problems using R programming.
3. Solving mixed constraints problems – Big M & Two phase method using TORA.
4. Solving transportation problems using R.
5. Solving assignment problems using R.
6. Solving optimization problems using LINGO.
7. Studying Primal-Dual relationships in LP using TORA.
8. Solving LP problems using dual simplex method using TORA.
9. Sensitivity & post optimality analysis using LINGO.
10 Solving shortest route problems using optimization software
11 Solving Project Management problems using optimization software
12 Testing random numbers and random variates for their uniformity.
13. Testing random numbers and random variates for their independence
14. Solve single server queuing model using simulation software package.
15. Solve multi server queuing model using simulation software package.

30 PERIODS

TOTAL: 60 PERIODS

COURSE OUTCOMES: On successful completion of this course, the student will able to
CO1: Formulate and solve linear programming problems (LPP)
CO2: Evaluate Integer Programming Problems, Transportation and Assignment Problems.
CO3: Obtain a solution to network problems using CPM and PERT techniques.
CO4: Able to optimize the function subject to the constraints.
CO5: Identify and solve problems under Markovian queuing models

TEXT BOOKS:
1. Hamdy A Taha, Operations Research: An Introduction, Pearson, 10th Edition, 2017.

REFERENCES:
1. ND Vohra, Quantitative Techniques in Management, Tata McGraw Hill, 4th Edition, 2011.
2. J. K. Sharma, Operations Research Theory and Applications, Macmillan, 5th Edition, 2012.
3. Hiller F.S, Liberman G.J, Introduction to Operations Research, 10th Edition McGraw Hill, 2017.
4. Jit. S. Chandran, Mahendran P. Kawatra, KiHoKim, Essentials of Linear Programming, Vikas Publishing House Pvt.Ltd. New Delhi, 1994.
5. Ravindran A., Philip D.T., and Solberg J.J., Operations Research, John Wiley, 2nd Edition, 2007.