lesson plan nba-operations research

8/19/2019 Lesson Plan NBA-Operations Research

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Lesson Plan

Semester: Year: 2015-16

Subject Name: Operations Research Subject Code: 10CS661

Total Teaching Hours: 52 hrs Duration of Exam: 3 hrs

Exam Marks: 100 IA Marks: 25

Lesson Plan Author : Sunil M E and Pradeep K Date: 04-01-2016

Checked By: Date:

Prerequisites:

Student should have the knowledge of the fundamentals of

1. Engineering Mathematics – Basic Mathematics.

Subject Learn ing Objectives: At the end of the Lesson the student should be able to:

1. Recognize, classify & use various models for solving a problem under consideration.2. Understand the fundamental concepts & general mathematical structure of a linear

programming model.

3. Convert an LP problem in to its standard form by adding sack, surplus & artificialvariables

4. Interpret the optimal solution of LP problems using simplex algorithm.5. Recognize the special cases such as degeneracy, multiple optimal solutions, unbounded

& infeasible solutions

6.

Formulate the dual LP problem & understand the relationship between primal & dual LP problems.

7. Perform sensitivity analysis on various parameters in an LP model without effecting the

optimal solution.8. Introduce a new variable & a constraint in the existing LP model with the reformulation.

9. Examine multiple optimal solution & prohibited routes in the transportation problem.

10. Solve the profit maximization transportation problem11. Solvean assignment problem using Hungarian method.

12. Understand how optimal strategies are formulated in the conflict & competitive

environment & the principle of Zero sum, two person games.

13. Apply min-max & max-min principle to compute the value of the game when there is a

saddle point.14. Understand the nature of Metaheuristics, Tabu search


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Subject Articulation Matrix: Mapping of Subject Learning Objectives (SLO) with Abet 3a to 3k

Criterion (semester outcomes)

Subject Name: Course code: Semester:

Year: (Odd Sem)

Subject Learning Objectives-

SLO

a b C D e f g h i j k

A p p l y m a t h , s c i e n c e

& e n g i n e e r i n g

D e s i g n & c o n d u c t

e x p e r i

e n t s

D e s i g n a s y s t e m ,

c o

p o n e n t

F u n c t i o n o n m u l t i -

d i s c i p l i n a r y t e a

s

I d e n t i f y ,

f o r m u l a t e

s o l v e e n g . P r o b .

P r o f e s s i o n a l

e t h i c a l

C o m m u n i c a t e

I m p a c t o f e n g i g .

l

i

L i f e l o n g l e a r n i n g

C o n t e m p o r a r y

M o d e r n

e n g i n e e r i n g t o o l s

Recognize, classify & use

various models for

solving a problem underconsideration

H M

Understand thefundamental concepts &

general mathematical

structure of a linear

programming model.

H

Convert an LP problem in

to its standard form by

adding sack, surplus &artificial variables M

Interpret the optimalsolution of LP problems

using simplex algorithm. L

Recognize the special

cases such as degeneracy,

multiple optimal

solutions, unbounded &infeasible solutions

M

Formulate the dual LP problem & understand the

relationship between

primal & dual LP problems.

M


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Perform sensitivity

analysis on various

parameters in an LPmodel without effecting

the optimal solution.

L

Introduce a new variable

& a constraint in the

existing LP model withthe reformulation.

M

Examine multiple optimal

solution & prohibited

routes in the

transportation problem.

M

Solve the profitmaximization

transportation problem M

Solve an assignment

problem using Hungarian

method. H

Understand how optimal

strategies are formulated

in the conflict &competitive environment

& the principle of Zero

sum, two person games.

M

Apply min-max & max-

min principle to computethe value of the game

when there is a saddle

point.

M M

Understand the nature of

Metaheuristics, Tabu

search M

Degree of compliance L: Low M: Medium H: High


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Syllabus Content

Subject Code: 10CS661 L-T-P: 4-0-0

Subject Name: Operations Research IA: 25

Teaching Hours: 52 Exam Marks: 100

Part – A

Introduction, Linear Programming – 1: Introduction: The origin, natureand impact of OR;Defining the problem and gathering data; Formulating amathematical model; Deriving solutions

from the model; Testing the model;Preparing to apply the model; Implementation .

Introduction to Linear Programming: Prototype example; The linear programming (LP) model.

06 hours

LP – 2, Simplex Method – 1: Assumptions of LP; Additional examples.The essence of the simplex

method; Setting up the simplex method; Algebraof the simplex method; the simplex method in

tabular form; Tie breaking inthe simplex method07 hours

Simplex Method – 2: Adapting to other model forms; Post optimality analysis; Computer

implementation. Foundation of the simplex method. 06 hours

Simplex Method – 2, Duality Theory: The revised simplex method, afundamental insight.

The essence of duality theory; Economic interpretation of duality, Primal dual relationship;

Adapting to other primal forms 07 hours

Part – B

Duality Theory and Sensitivity Analysis, Other Algorithms for LP : The role of duality in

sensitive analysis; The essence of sensitivity analysis;Applying sensitivity analysis. The dual

simplex method; Parametric linear programming; The upper bound technique07 hours

Transportation and Assignment Problems: The transportation problem; A streamlined simplex

method for the transportation problem; The assignment problem; A special algorithm for the

assignment problem.07 hours

Game Theory, Decision Analysis: Game Theory: The formulation of two persons, zero sum games;

Solving simple games- a prototype example; Games with mixed strategies; Graphical solution

procedure; Solving by linear programming, Extensions. Decision Analysis: A prototype example;

Decision making without experimentation; Decision making with experimentation; Decision trees.

06 hours

Metaheuristics: The nature of Metaheuristics, Tabu Search, Simulated

Annealing, Genetic Algorithms. 06hours


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Text Books

1. Frederick S. Hillier and Gerald J. Lieberman: Introduction to Operations Research:Concepts and Cases, 8th Edition, TataMcGraw Hill, 2005.

(Chapters: 1, 2, 3.1 to 3.4, 4.1 to 4.8, 5, 6.1 to 6.7, 7.1 to 7.3, 8, 13,

14, 15.1 to 15.4)

Reference Books

1. Wayne L. Winston: Operations Research Applications andAlgorithms, 4th Edition,

Cengage Learning, 2003.

2. Hamdy A Taha: Operations Research: An Introduction, 8th Edition,

Pearson Education, 2007.

Evaluation SchemeI A Scheme

Assessment Weightage in

Marks

Internal Assessment Exam 1 25

Internal Assessment Exam 2 25

Improvement- Internal Assessment Exam 3 25

Assignments ---

Total 25

Subject Uni tization for IA Exams and Semester Examination

Unit ChapterTeaching

Hours

No. of Questions in No. of Questions

ExamIA Exam I IA Exam II

Part

- A

1 08

VTU Exam

Pattern

VTU Exam

PatternVTU Exam

Pattern

2 06

3 06

4 06

Part

- B

5 08

6 06

7 068 06

Answer any

two questions

Answer any

two questions

Answer any 2

questions from

part A, Part B

and 1 from

either Part A or

Part B


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Note

Each Question carries 20 marks and may consist of sub-questions.

Mixing of sub-questions from different chapters within a unit (only for Unit I and Unit I I ) is allowed in IA

I, II and Semester Exam.

Answer 5 full questions of 20 marks each (two ful l questions from Part A, Part B, and 1 ful l question

fr om Either Part A of Part B ) out of 8 in Semester Exam.

Date: Head of Department

Unit wise PlanUnit - I

Subject Code and Name: 10CS661& Operations Research

Unit Number and Title : Unit 1 - Introduction, Linear Programming – 1 Planned Hours: 06 hrs

Lesson Schedule

Class No. Portion covered per hour

1) Introduction: The origin, nature and impact of OR

2)

Defining the problem and gathering data; Formulating a mathematical model3) Deriving solutions from the model; Testing the model;Preparing to apply the model;

4) Implementation.Introduction to Linear Programming: Prototype example;5) The linearprogramming (LP) model.

6) The linearprogramming (LP) model.

At the end of this chapter student should be able to:

1. Understand the need of using Operations Research.

2.

Know the historical perspective of Operations Research approach.

3. Recognize, classify & use various models for solving a problem under consideration.4. Understand the fundamental concepts & general mathematical structure of a linear

programming model.

Review Questions (Bloom’s taxonomy Level 1 – Knowledge and Level 2 - Comprehension)


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1. Define Operations Research.(L1)

2. Explain the six phases of the OR study. (L2)

3. Define the following terms: Objective function, constraint, optimization(L1)4. Explain the origin OR (L2)

5. Discuss the advantages of OR study

Critical Questions (Bloom’s taxonomy Level 3 – Application and Level 4 - Analysis)

1. A retailer deals in two items only, item A and item B. he has 50,000 to invest and a spaceto store at most 60 pieces. An item A costs him 2,500 and B costs him 500. A net profit

to him on item A is 500 and item B is 150. If he can sell all the items he purchases, how

should he invest his amount to have maximum profit?(i) Give mathematical formulation to the LPP

(ii) Use graphical method to solve the problem.(L3)

2. Solve the following LPP using graphical method.

Maximize Z=100X1 + 40X2 Subject to constraints, 5X1 + 2X2


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man-days for lettuce. A total of 400 man days of labor available at Rs 20 per man day

formulate the problem as linear programming problem model to maximize the farmers’

total profit.

6. A Manufacturer of biscuits is considering 4 types of gift packs containing 3 types of

biscuits, orange cream (oc), chocolate cream (cc) and wafer’s(w) market research studyconducted recently to assess the preferences of the consumers shows the following typesof assortments to be in good demand.

7. Solve using Graphical Method

8. Solve using Graphical Method


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9. Find the maximum value of Given LPP

10. Find the maximum value of Given LPP

Challenging Questions(Bloom’s taxonomy Level 5 – Synthesis and Level 6 - Evaluation)1. Solve the following LPP using graphical method.

Minimize Z = 20X1 + 10X2 Subject to constraints, X1 + 2X2=30

4X1 + 3X2>=60 and X1,X2>=0 (L5) 2.

3.


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Case Studies / Mini Projects(Bloom’s taxonomy Level 5– Synthesis and Level 6 -

Evaluation)

Unit wise PlanUnit - VI

Subject Code and Name: 10CS661& Operations Research

Unit Number and Title: Uni t 6Transportation and Assignment Problems Planned Hours: 07 hrs

Lesson Schedule

Class No. Portion covered per hour

1) The transportation problem2) The transportation problem

3) streamlined simplex method for the transportation problem

4) streamlined simplex method for the transportation problem

5) The assignmentproblem; A special algorithm for the assignment problem6) The assignmentproblem; A special algorithm for the assignment problem

7)

The assignmentproblem; A special algorithm for the assignment problem

Learni ng Objectives (Note: Ensure that each topic in a uni t has a learn ing objective. I f there are 6 topics in a

uni t, there must be min imum of 6 l earni ng objectives. I t can have more than 6 also)

At the end of this chapter student should be able to:

1. Recognize & formulate a transportation problem involving a large number of shipping

routes.2. Drive initial feasible solution using several methods & optimal solution using modified

distribution method.3. Examine multiple optimal solution & prohibited routes in the transportation problem.4. Solve the profit maximization transportation problem.5. Formulate an assignment problem as a square matrix.

6. Apply the Hungarian method to solve an assignment problem.7.

Solve a travelling salesman problem.


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Review Questions (Bloom’s taxonomy Level 1 – Knowledge and Level 2 - Comprehension)

1. Explain different steps in Hungarian algorithm to solve an assignment problem.(L2)2. Explain Hungarian algorithm with an example. (L1)

Critical Questions (Bloom’s taxonomy Level 3 – Application and Level 4 - Analysis)

Findthe optimal transportation cost of the following matrix by using Least CostMethod.(L3)

Challenging Questions (Bloom’s taxonomy Level 5– Synthesis and Level 6 - Evaluation)

(L5)

3. Solve the following transportation problem by North-West corner rule, Row Minima,

Column Minima, Matrix Minima and VAM Method:


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4. There are 3 Parties who supply the following quantity of coal P1= 14t, P2=12t, P3= 5t.

There are 3 consumers who require the coal as follows C1=6t, C2=10t, C3=15t. The cost

matrix in Rs. Per ton is as follows. Find the schedule of transportation policy which

minimises the cost:

5.

6. A company has three plants supplying the same product to the five distribution centers.Due to peculiarities inherent in the set of cost of manufacturing, the cost/ unit will vary


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from plant to plant. Which is given below. There are restrictions in the monthly capacity

of each plant, each distribution center has a specific sales requirement, capacity

requirement and the cost of transportation is given below.

The cost of manufacturing a product at the different plants is Fixed cost is Rs 7x105, 4x

105 and 5x 105. Whereas the variable cost per unit is Rs 13/-, 15/- and 14/- respectively.Determine the quantity to be dispatched from each plant to different distribution centers,

satisfying the requirements at minimum cost.

7.


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Case Studies / Mini Projects (Bloom’s taxonomy Level 5– Synthesis and Level 6 -

Evaluation)


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lesson plan nba-operations research

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