15AE751 OPERATIONS RESEARCH syllabus for AE

Introduction:

Evolution of OR, definition of OR, scope of OR, application areas of OR, steps (phases) in OR study, characteristics and limitations of OR, models used in OR, linear programming (LP) problemformulation and solution by graphical method.

Solution of Linear Programming Problems:

The simplex methodcanonical and standard form of an LP problem, slack, surplus and artificial variables, big M method and concept of duality, dual simplex method.

Transportation Problem:

Formulation of transportation problem, types, initial basic feasible solution using different methods, optimal solution by MODI method, degeneracy in transportation problems, application of transportation problem concept for maximization cases. Assignment Problem-formulation, types, application to maximization cases and travelling salesman problem

Integer Programming:

Pure and mixed integer programming problems, solution of Integer programming problems-Gomory’s all integer cutting plane method and mixed integer method, branch and bound method, ZeroOne programming.

Pert-CPM Techniques:

Introduction, network construction - rules, Fulkerson’s rule for numbering the events, AON and AOA diagrams; Critical path method to find the expected completion time of a project, floats; PERT for finding expected duration of an activity and project, determining the probability of completing a project, predicting the completion time of project; crashing of simple projects

Queuing Theory:

Queuing systems and their characteristics, Pure-birth and Pure-death models (only equations), empirical queuing models – M/M/1 and M/M/C models and their steady state performance analysis.

Game Theory:

Formulation of games, types, solution of games with saddle point, graphical method of solving mixed strategy games, dominance rule for solving mixed strategy games.

Sequencing:

Basic assumptions, sequencing ‘n’ jobs on single machine using priority rules, sequencing using Johnson’s rule-‘n’ jobs on 2 machines, ‘n’ jobs on 3 machines, ‘n’ jobs on ‘m’ machines. Sequencing 2 jobs on ‘m’ machines using graphical method.

Course outcomes:

After studying this course, students will be able to:

1. Apply the basic of operations research.

2. Classify the PERT-CPM techniques, queuing theory and game theory.

3. Identify the sequencing techniques.

Graduate Attributes :

• Engineering Knowledge.
• Problem Analysis.
• Design / development of solutions
• Interpretation of data

Question paper pattern:

• The question paper will have ten questions.
• Each full question consists of 16 marks.
• There will be 2 full questions (with a maximum of four sub questions) from each module.
• Each full question will have sub questions covering all the topics under a module.
• The students will have to answer 5 full questions, selecting one full question from each module.

Text Books:

1. P K Gupta and D S Hira ,Operations Research, Chand Publications, New Delhi , Revised edition,2007,ISBN-13: 978-8121902816

2. Taha H A ,Operations Research,Pearson Education,9th edition,2014,ISBN-13: 978-9332518223

Reference Books:

1. A P Verma ,Operations Research, S K Kataria &Sons, 2012,ISBN-13: 978-9350142400

2. Paneerselvan ,Operations Research, PHI,2nd edition,2009,ISBN-13: 978-8120329287

3. A M Natarajan, P Balasubramani, Operations Research, Pearson Education, 1st edition,2011,ISBN13: 978-8131767764

4. Hillier and Liberman, Introduction to Operations Research, 8th Ed., McGraw Hill

5. S.D. Sharma ,Operations Research, , Kedarnath Ramanath & Co, 2012,ISBN-13: 978-9380803388