Operations research is the application of analytical methods to help decision-makers choose optimal courses of action. It originated during World War II and uses mathematical techniques like linear programming, non-linear programming, and stochastic programming to optimize resource allocation. Linear programming involves maximizing or minimizing a linear objective function subject to linear constraints. Examples of linear programming problems include product mix problems, blending problems, and production scheduling problems.

1. OPERATIONS RESEARCH
OPERATIONS RESEARCH
By
DR. NEHA GUPTA
FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY
19 June 2016
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 1 / 11

2. OPERATIONS RESEARCH
Intoduction
Components of Quantitative Techniques
QUANTITATIVE
TECHNIQUES
STATISTICS
OPERATIONS
RESEARCH
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 2 / 11

3. OPERATIONS RESEARCH
Intoduction
What is Operations Research?
Operations Research is the application of analytical methods designed to help the
decision makers choose between various courses of action available to
accomplish specified objectives.
It represents the study of optimal resource allocation.
In simple terms, it is described as the Science of Better.
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 3 / 11

4. OPERATIONS RESEARCH
Intoduction
What is Operations Research?
Operations Research is the application of analytical methods designed to help the
decision makers choose between various courses of action available to
accomplish specified objectives.
It represents the study of optimal resource allocation.
In simple terms, it is described as the Science of Better.
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 3 / 11

5. OPERATIONS RESEARCH
Intoduction
What is Operations Research?
Operations Research is the application of analytical methods designed to help the
decision makers choose between various courses of action available to
accomplish specified objectives.
It represents the study of optimal resource allocation.
In simple terms, it is described as the Science of Better.
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 3 / 11

6. OPERATIONS RESEARCH
Intoduction
What is Operations Research?
Operations Research is the application of analytical methods designed to help the
decision makers choose between various courses of action available to
accomplish specified objectives.
It represents the study of optimal resource allocation.
In simple terms, it is described as the Science of Better.
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 3 / 11

7. OPERATIONS RESEARCH
Intoduction
Operations Research (OR)
The field of Operations Research (OR) originated in the period immediately prior to and
during the Second World War.
Operations Research is a bouquet of mathematical techniques that have evolved over
the last six decades to improve the process of business decision making.
Operations Research offers tools to optimize and find the best solutions to myriad
decisions that managers have to take in their day to day operations or while carrying
out strategic planning.
Today, with the advent of operations research software, these tools can be applied by
managers even without any knowledge of the mathematical techniques that underlie
the solution procedures.
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 4 / 11

8. OPERATIONS RESEARCH
Intoduction
Operations Research (OR)
The field of Operations Research (OR) originated in the period immediately prior to and
during the Second World War.
Operations Research is a bouquet of mathematical techniques that have evolved over
the last six decades to improve the process of business decision making.
Operations Research offers tools to optimize and find the best solutions to myriad
decisions that managers have to take in their day to day operations or while carrying
out strategic planning.
Today, with the advent of operations research software, these tools can be applied by
managers even without any knowledge of the mathematical techniques that underlie
the solution procedures.
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 4 / 11

9. OPERATIONS RESEARCH
Intoduction
Operations Research (OR)
The field of Operations Research (OR) originated in the period immediately prior to and
during the Second World War.
Operations Research is a bouquet of mathematical techniques that have evolved over
the last six decades to improve the process of business decision making.
Operations Research offers tools to optimize and find the best solutions to myriad
decisions that managers have to take in their day to day operations or while carrying
out strategic planning.
Today, with the advent of operations research software, these tools can be applied by
managers even without any knowledge of the mathematical techniques that underlie
the solution procedures.
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 4 / 11

10. OPERATIONS RESEARCH
Intoduction
Operations Research (OR)
The field of Operations Research (OR) originated in the period immediately prior to and
during the Second World War.
Operations Research is a bouquet of mathematical techniques that have evolved over
the last six decades to improve the process of business decision making.
Operations Research offers tools to optimize and find the best solutions to myriad
decisions that managers have to take in their day to day operations or while carrying
out strategic planning.
Today, with the advent of operations research software, these tools can be applied by
managers even without any knowledge of the mathematical techniques that underlie
the solution procedures.
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 4 / 11

11. OPERATIONS RESEARCH
Intoduction
Operations Research-Methodology
OPERATIONS
RESEARCH
PROBLEM
ANALYSIS
SOLUTION
DEVEL-
OPMENT
SOLUTION
VALIDATION
IMPLEMENTATIONEVALUATION
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 5 / 11

12. OPERATIONS RESEARCH
Societies and Journals of Operations Research
Techniques of Operations Research
Linear Programming
Non-Linear Programming
Stochastic Programming
Queueing Theory
Inventory Theory
Game Theory
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 6 / 11

13. OPERATIONS RESEARCH
Societies and Journals of Operations Research
Linear Programming
Linear Programming deals with the optimization (i.e., maximize or minimize) of a linear
function called Objective function under the set of given linear equalities or inequalities
called Constraints.
The linear programming model can be written in notation as:
Maximize (or Minimize) Z =
n
j=1
cj xj
subject to
n
j=1
aij xj {≤, =, ≥} bi ∀ i = 1, 2, . . . , m
and xj ≥ 0 ∀ j = 1, 2, . . . , n



(1)
where bi are the parameters of LPP and one and only sign among ≤, =, ≥ holds true
for each i.
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 7 / 11

14. OPERATIONS RESEARCH
Societies and Journals of Operations Research
Examples of LP Problems
A Product Mix Problem
A manufacturer has fixed amounts of different resources such as raw material,
labor, and equipment.
These resources can be combined to produce any one of several different
products.
The quantity of the ith resource required to produce one unit of the jth product is
known.
The decision maker wishes to produce the combination of products that will
maximize total income.
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 8 / 11

15. OPERATIONS RESEARCH
Societies and Journals of Operations Research
Examples of LP Problems (Contd.)
A Blending Problem
Blending problems refer to situations in which a number of components (or
commodities) are mixed together to yield one or more products.
Typically, different commodities are to be purchased. Each commodity has known
characteristics and costs.
The problem is to determine how much of each commodity should be purchased
and blended with the rest so that the characteristics of the mixture lie within
specified bounds and the total cost is minimized.
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 9 / 11

16. OPERATIONS RESEARCH
Societies and Journals of Operations Research
Examples of LP Problems (Contd.)
A Production Scheduling Problem
A manufacturer knows that he must supply a given number of items of a certain
product each month for the next n months.
They can be produced either in regular time, subject to a maximum each month,
or in overtime. The cost of producing an item during overtime is greater than
during regular time. A storage cost is associated with each item not sold at the
end of the month.
The problem is to determine the production schedule that minimizes the sum of
production and storage costs.
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 10 / 11

17. OPERATIONS RESEARCH
Societies and Journals of Operations Research
FOR YOUR ATTENTION
ByDR. NEHA GUPTA (FACULTY OF COMMERCE & MANAGEMENT, SGT UNIVERSITY)OPERATIONS RESEARCH 19 June 2016 11 / 11