This document provides an introduction to operations research. It discusses how operations research uses quantitative methods and mathematical modeling to help solve complex problems in engineering and management. Some key points covered include: - Operations research originated from efforts during World War II to apply scientific methods to military problems. - It involves constructing mathematical models of real-world systems and using analytical techniques like linear programming to derive optimal solutions. - Common applications include production and distribution planning, investment analysis, and facility layout. - The modeling process involves formulating the problem, developing and testing a model, and implementing the results. - Operations research has helped many organizations save millions of dollars by optimizing resource allocation and other business decisions.

1. 1Slide
Lecture #1Lecture #1
Introduction to OperationsIntroduction to Operations
ResearchResearch
ByBy
Dr. Ehtesham HussainDr. Ehtesham Hussain
ehussain@uok.edu.pkehussain@uok.edu.pk
Associate ProfessorAssociate Professor
Department of StatisticsDepartment of Statistics
University of KarachiUniversity of Karachi

2. 2Slide
Operations Research (American)Operations Research (American)
Operational Research (Britisher)Operational Research (Britisher)
Now-a-daysNow-a-days referred asreferred as
Management ScienceManagement Science
In brief:
OR
MS

3. 3Slide
Books:Books:
1.1. Taha, H.A;Taha, H.A;
Operations Research An introductionOperations Research An introduction
Macmillan.Macmillan.
2. Bronson, R.2. Bronson, R.
Operations ResearchOperations Research
Schaum outline series, Mc Grow-HillSchaum outline series, Mc Grow-Hill
3. Hiller, F.S and G, J. Lieberman;3. Hiller, F.S and G, J. Lieberman;
Introduction to Operations ResearchIntroduction to Operations Research
Holden-Day, Inc; San FranciscHolden-Day, Inc; San Francisc
4. William Peacock;4. William Peacock;
Quantitative MethodsQuantitative Methods for Management Decisions.for Management Decisions.
Wiley. Jan.Wiley. Jan.

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Several Friendly Spread SheetSeveral Friendly Spread Sheet
Programs are available on CDs.Programs are available on CDs.
 ToraTora
 LindoLindo
 Quality Management etc.Quality Management etc.

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Brief History:Brief History:
The subject of Operation Research is conceive fromThe subject of Operation Research is conceive from
Word War II.Word War II.
During World War II, British military leaders askedDuring World War II, British military leaders asked
scientists and engineers to analyze several militaryscientists and engineers to analyze several military
problems:problems:
The development of radar and management ofThe development of radar and management of
convoy, bombing, antisubmarine and miningconvoy, bombing, antisubmarine and mining
operations,operations,
The application of mathematics and the scientificThe application of mathematics and the scientific
method to military operations was called operationsmethod to military operations was called operations
research.research.

6. 6Slide
Operations Research (OR)Operations Research (OR)
 Is the study of how to form mathematicalIs the study of how to form mathematical
methods of complex engineering andmethods of complex engineering and
management problems, and how to analyzemanagement problems, and how to analyze
them to gain insight about possiblethem to gain insight about possible
solutions.solutions.

7. 7Slide
 The field of operations research, orThe field of operations research, or
management science (MS), ismanagement science (MS), is
concerned with the development andconcerned with the development and
application of quantitative analyses toapplication of quantitative analyses to
the solution of problems faced bythe solution of problems faced by
managers of public and privatemanagers of public and private
organizations.organizations.

8. 8Slide
 Operations research may be describedOperations research may be described
as a scientific approach to decisionas a scientific approach to decision
making that involves the operations ofmaking that involves the operations of
organizational systems.organizational systems.

9. 9Slide
OperationOperation
Operation is the process of transformingOperation is the process of transforming
inputs into outputs and thereby addinginputs into outputs and thereby adding
value to some entity; this constitutes thevalue to some entity; this constitutes the
primary function of virtually everyprimary function of virtually every
organization.organization.

10. 10Slide
In Operations Research we tackleIn Operations Research we tackle
problems like:problems like:
 Production and distribution at minimum cost.Production and distribution at minimum cost.
 Maximum profit plan.Maximum profit plan.
 Cheapest way to ship the goods.Cheapest way to ship the goods.
 Planning work shifts for large organizations.Planning work shifts for large organizations.
 Designing facilities for customer service.Designing facilities for customer service.
 Choosing investments for available funds.Choosing investments for available funds.
 Budget Allocation Problems etc.Budget Allocation Problems etc.

11. 11Slide
What Operations Researchers,What Operations Researchers,
Statistician, Mathematician andStatistician, Mathematician and
Computer Scientist want to do?Computer Scientist want to do?
Since we are living in continuouslySince we are living in continuously
changing world they want to capture thechanging world they want to capture the
behaviors of this world by Mathematicalbehaviors of this world by Mathematical
ModelsModels

12. 12Slide
A mathematical model is the collection ofA mathematical model is the collection of
variables and relationships needed tovariables and relationships needed to
describe pertinent features of such adescribe pertinent features of such a
problem.problem.
Mathematical model:

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Steps:Steps:
Formulating the problem:Formulating the problem:
 Constructing a mathematical model to represent theConstructing a mathematical model to represent the
system under study.system under study.
 Deriving a solution from the model.Deriving a solution from the model.
 Testing the model and the solution derived from it.Testing the model and the solution derived from it.
 Establishing controls over the solutions.Establishing controls over the solutions.
 Putting the solution to work: implementation.Putting the solution to work: implementation.

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The Modeling Process:The Modeling Process:
Real System Model
Model
conclusion
Real
Conclusion
Formulation
Interpretation

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Modeling The Real WorldModeling The Real World
Defining the problem
Developing a model
Acquiring input data
Developing a solution
Testing the solution
Analyzing the results
Implementing the Results

16. 16Slide
Types of MathematicalTypes of Mathematical
Programming ModelsProgramming Models
 Linear programming (L.P).Linear programming (L.P).
 Non-linear programming.Non-linear programming.
 Integer programming.Integer programming.
Dynamic programming.Dynamic programming.

17. 17Slide
L.P is most frequently used to allocate limited
or scarce resources. Some allocation problems
tackled by this method are:
 Product mix problems.
 Component mix problems.
 Problems of financial budgeting and planning.
 Routing and logistic.

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A central theme in OR is the
optimal allocation of scarce
Resources

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Benefits of using ORBenefits of using OR
TechniquesTechniques ::
Organizations Are SavingOrganizations Are Saving
Millions of Dollars.Millions of Dollars.
See photo state MaterialSee photo state Material

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Mathematical Model for ProfitMathematical Model for Profit
WE NEED TO KNOWWE NEED TO KNOW
1. Expenses (Total Cost)1. Expenses (Total Cost)
2. Revenue2. Revenue
3. Profit3. Profit
Total cost = Fixed cost – Variable cost per unit * number of unitsTotal cost = Fixed cost – Variable cost per unit * number of units
sold.sold.
Let X be the number of unitsLet X be the number of units
TC(X) = A + BXTC(X) = A + BX
Revenue = sold price * number of units soldRevenue = sold price * number of units sold
R(X) = P * XR(X) = P * X
Profit = Revenue – Total CostProfit = Revenue – Total Cost
Y = R (X)- TC(X)Y = R (X)- TC(X)

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We can find many otherWe can find many other
relevant information likerelevant information like
Break Even PointsBreak Even Points
BEV = Y = 0BEV = Y = 0

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For IllustrationFor Illustration
A factory has fixed overheads of pond 2000 perA factory has fixed overheads of pond 2000 per
week and manufactures pencils which it sellsweek and manufactures pencils which it sells
for 50p each. If the raw materials and labourfor 50p each. If the raw materials and labour
necessary to make a pencils are estimated tonecessary to make a pencils are estimated to
cost 30p,how many of them should thecost 30p,how many of them should the
company sell each week in order tocompany sell each week in order to break evenbreak even??

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SolutionSolution
Let x stand for the number of pencils sold each week.Let x stand for the number of pencils sold each week.
Revenue? , Expenditure?Revenue? , Expenditure?
R=0.5xR=0.5x
E=0.3x+2000E=0.3x+2000