Operations Research provides a quantitative technique to the

executives for better decisions for operation under their control.

Developed during the World War II.

Limited military resources.

Efficient allocation of resources was

required.

Large number scientists invited .

The efforts of the team helped in

winning the battle.

The name “OR” directly derived from

“Research on Military Operations”.

The success encouraged the scientists.

They moved to different sectors e.g.,

transportation, health, education, etc.

OR in India started in 1949.

Regional Research Laboratory opened in

Hyderabad.

Industry

Transportation

Banking and Finance

Agriculture

Defense

Systems Approach

Inter-disciplinary Team Approach

Methodological Approach

Operations Economy

Finance, Budgeting and Investments

Purchasing, Procurement and Exploration

Production Management

Marketing Management

Personnel Management

Research and Development

Judgement Phase

i. Establishment of Objectives

ii. Determination of measures

iii. Formulation of Problems

Research Phase

i. Data Collection

ii. Model formulation

iii. Analysis and Predictions

Action Phase

i. Making Recommendations

Better planning

Flexibility in operations

Better co-ordination

Better decisions

Better systems

Analytic Or Deductive

Method

Numerical Or Iterative

Method

Monte Carlo Method

ISOLATION OF

MANAGEMENT PROBLEM

PROBLEM FORMULTION

REAL WORLD

ISOLATION OF

MANAGEMENT PROBLEM

PROBLEM FORMULATION

REAL WORLD

QUALI-TATIVE MODEL

QUAN-TATIVE MODEL

MODEL BUILDING

MODEL REFINEM-

ENT

ISOLATION OF

MANAGEMENT PROBLEM

PROBLEM FORMULATION

REAL WORLD

QUALI-TATIVE MODEL

QUAN-TATIVE MODEL

MODEL BUILDING

MODEL REFINEM-

ENT

MODEL TESTING

TEST-ING

SYSTEMDATA COLLECTION

ISOLATION OF

MANAGEMENT PROBLEM

PROBLEM FORMULATION

REAL WORLD

QUALI-TATIVE MODEL

QUAN-TATIVE MODEL

MODEL BUILDING

MODEL REFINEM-

ENT

MODEL TESTING

TEST-ING

SYSTEM

ESTABLISH-ING CONTROLS

CONCLUS-IONS &

IMPLEMENTATION

DATA COLLECTION

Linear Programming

Decision Models

Integer Programming

Dynamic Programming

Stochastic Programming

Magnitude of computation

Absence of quantification

Conventional thinking

Money and time costs

Implementation

The analysis of problems

Linear function of a number of

variables is to be maximized or

minimized

Variables are subject to a number of

restraints in the form of linear

inequalities.

Proportionality

Certainty

Additivity

Divisibility

Non-negativity

General form of a LPP Optimize (Maximize or Minimize) Z=c1x1+c2x2……cnxn

Subject to linear constraints a11x1+a12x2+…….a1nxn(<,=,>)b1

a21x1+a22x2+…….a2nxn(<,=,>)b2

. . .

. . .

am1x1+am2x2+…….amnxn(<,=,>)bm

And x1,x2,x3……….xn >0

General form of a LPP Optimize (Maximize or Minimize) Z=c1x1+c2x2……cnxn

Subject to linear constraints a11x1+a12x2+…….a1nxn(<,=,>)b1

a21x1+a22x2+…….a2nxn(<,=,>)b2

. . .

. . .

am1x1+am2x2+…….amnxn(<,=,>)bm

And x1,x2,x3……….xn >0

OBJECTIVE FUNCTION

General form of a LPP Optimize (Maximize or Minimize) Z=c1x1+c2x2……cnxn

Subject to linear constraints a11x1+a12x2+…….a1nxn(<,=,>)b1

a21x1+a22x2+…….a2nxn(<,=,>)b2

. . .

. . .

am1x1+am2x2+…….amnxn(<,=,>)bm

And x1,x2,x3……….xn >0

OBJECTIVE FUNCTION

CONSTRAINTS

General form of a LPP Optimize (Maximize or Minimize) Z=c1x1+c2x2……cnxn

Subject to linear constraints a11x1+a12x2+…….a1nxn(<,=,>)b1

a21x1+a22x2+…….a2nxn(<,=,>)b2

. . .

. . .

am1x1+am2x2+…….amnxn(<,=,>)bm

And x1,x2,x3……….xn >0

OBJECTIVE FUNCTION

CONSTRAINTS

NON-NEGATIVE RESTRICTIONS

Two Phase Procedure

Phase I1.Verbalize the problem and its structure.2.Determine Overall Structure.3.Determine restricting factors.

Phase II

1. Define Decision Variables.

2. Identify contribution coefficients(cj’s)

associated with each variable

3. Formulate the objective function.

4. Identify physical rate of substitution

coefficients(ai j’s).

5. Identify the available resources (bi’s).

6. Maintain non-negativity condition.

DECISION VARIABLE

ARTICLE HOURS ON MACHINE

HOURS ON CRAFTSMAN

PROFIT PER UNIT

X1 A 1.5 2 Rs. 50

X2 B 2.5 1.5 Rs.40

Hours Available (per week)

80Maximum

70Maximum

Objective FunctionMaximize Z=50x1 + 40x2

Constraints Time for article A + Time for article B <

Available time on M/cFor Machine-

1.5x1 + 2.5x2 <80

For Craftsman- 2x1 + 1.5x2<70

Non-Negativity Constraints x1,x2 >0

DIET DECISION VARIABLE

TIME FOR ARRANGIN

G RAW MATERIALS

TIME FOR COOKING

PROFIT PER

UNIT

Rice x1 5 min. 10 min. Rs. 2

Chapati x2 15 min. 15 min. Rs. 5

Minutes available per week

120 min. 60 min.