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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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