BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE- PILANI, K. K. Birla GOA CAMPUS INSTRUCTION DIVISION

FIRST SEMESTER 2012-2013 Course Handout Part II

Date: 03.08.2012 In addition to part-I (General Handout for all courses appended to the time table), this portion gives further specific details regarding the course.

Course No. : AAOC C222 Course Title : OPTIMIZATION Instructor-in-charge : P. DHANUMJAYA Instructors : Anil Kumar, Manoj Kumar Pandey, Mayank Goel, Sangeeta Jaiswal, Prabal Paul

1. Scopes and Objective of the Course:

An optimization problem in its simple form is one in which some entity with or without being

subjected to certain constraints is minimized or maximized. The entity to be optimized may be profit, cost, time, product efficiency, consumer utility, etc. The constraints may involve manpower, availability of space, raw materials, funds, machine capabilities, government controls, etc.

The subject of optimization is multidisciplinary in nature. Optimization Problems are encountered in physical sciences, engineering, economics, industry, planning, and many other areas of human activity. Background needed for undertaking this course is acquaintance with Calculus, Set Theory and Linear Algebra. Objective of the Course is to familiarize the student with standard methods of solving optimization problems.

2. Text Book:

Hamdy A. Taha, Operations Research: An Introduction, Pearson 9th Edition, 2012.

3. Reference Books:

R1. Ronald L. Rardin, Optimization in Operations Research, Pearson, First Indian Reprint 2002.

R2. F. S. Hillier and G. J. Lieberman, Introduction to Operations Research, T M H, 8th.edn., 2005.

R3. Winston, Operations Research: Applications and Algorithms, Thomson, 3rd edn., 1996.

R4. H. A. Eiselt and C. L. Sandblom, Linear Programming and its Applications, Springer, 2011.

R5. Saul I. Gass, Linear Programming Methods and Applications, Dover Publications, 5th edn., 2003.

4. Course Plan:

Learning Objectives Topics to be covered Lect. No. Ref. To Text Book

To understand the meaning of Optimization

Introduction to optimization 1

How to develop Linear Programming models and how to solve two variables LP models by the graphical method

LP problems, Two variable LP model, Graphical LP solution, Convex Set

2-6 2.1, 2.2, 2.4, 7.1, 7.1.1

To obtain an understanding of why and how the simplex calculations are made and know how to recognize the special situations

LP model in equation form, Transition from graphical to algebraic solution The Simplex Method, Generalized simplex tableau in matrix form, Revised Simplex method Artificial starting solution, Special cases in the Simplex method

7-8

9-10

11-14

3.1, 3.2 3.3, 7.1.2, 7.2 3.4, 3.5

To understand the concept of duality, how to read and interpret the solution of dual problem and relate the dual solution to the primal solution and to explain how post optimal analysis can be used by a decision maker

Definition of Dual Problem, Duality, Primal-Dual Relationships, Economic Interpretation of Duality, Additional simplex algorithms (Dual Simplex Method, Generalized Simplex Algorithm), Post optimal Analysis

15-17

18-19

20-21

4.1, 7.4, 4.2 4.3, 4.4 4.5

To formulate transportation and assignment problems as LPP and how to solve these problems

Definition of transportation problem, The transportation Algorithm, The Assignment Model

22-24

25-26

5.1, 5.3 5.4

To understand Integer Programming problem and its efficacy

Formulation of IP problem Branch and Bound Algorithm, Cutting Plane method

27-29 9.1, 9.2

How to solve Nonlinear Programming problem

Unconstrained problems, Convex and concave functions, Elimination Methods: Direct search method Gradient of a Function, Descent Methods: Steepest Descent Method Karush-Kuhn-Tucker (KKT) Conditions, Quadratic Programming,

30

31-34

35

36-37

20.1, 20.1.1 21.1.1, 21.1.2 20.2.2 21.2.2

To understand multiples objectives optimization and how to solve multi objective optimization

Goal Programming Formulation, Goal Programming Algorithms: The weights Method and The Preemptive Method

38

39-40

8.1 8.2

5. Self Learning Component (SLC): Use TORA and MATLAB software's to solve optimization problems.

6. Evaluation Scheme:

Component Duration Weightage Date Time Venue

Test I 1 hr. 25 % 14-09-2012 8:30 – 9:30 AM **

Test II 1 hr. 25 % 27-10-2012 8:30 – 9:30 AM **

Compre. Exam. 3 hrs 40 % 04-12-2012 9:00 AM – 12:00 Noon **

Surprise Quiz/SLC/

Assignments

**

10%

**

**

**

** To be announced later.

7. Notices: All notices in relation to the above course will be put up on the Moodle Server only.

8. Make up Policy: Make up will be given only for genuine cases and for that prior permission has to be obtained from IC.

9. Chamber consultation hours: To be announced in tutorial class by the respective Instructor.

Instructor-in-charge

AAOC C222