Operations research is the application of scientific methods to complex problems involving large systems. It develops models of systems that incorporate factors like chance and risk to predict outcomes of decision strategies. The goal is to help management make scientifically informed policies. Some applications of operations research include finance, marketing, production management, and human resources. The document then provides an example problem solving the optimal allocation of newspaper advertisements to maximize exposure within a budget.

1. 1
Operation Research
IIMT SCHOOL OF MANAGEMENT
(ISM)
OPERATIONS RESEARCH
Semester – 2
Academic Year 2013-14
Module Leader
Ms. Navdeep Kaur Kular
Submitted By
Rishabh Shukla
Post Graduate Diploma in
Management

2. 2
Operations Research
Operations research is the application of the methods of science to complex
problems arising in the direction and management of large system of men,
machines, materials and money in industry, business, government and defense
(Sharma, 2013). The distinctive approach is to develop a scientific model of the
system, incorporating measurements of factor such as chance and risk, with which
to predict and compare the outcomes of alternatives decision strategies and
controls. The purpose is to help management, determine its policy and actions
scientifically.
Applications of Operations Research
• Finance and Accounting
 Cash flow analysis, Dividend policy, investment and portfolio
management, Balance sheet, Long-range capital requirement etc.
 Break-even analysis, capital budgeting, Credit policies, and financial
planning
 Claim and complaint procedure.
• Marketing
 Selection of production, competitive action, timing etc.
 Determine the optical production mix.
 Advertising, media planning and election.
 Scheduling a time for launching a new product.
 Size of the stock.

3. 3
Purchasing, Procurementand Exploration
▫ Transportation planning,
▫ Replacement policies
▫ Bidding policies and equipment replacement policies.
▫ Determining the quantity of purchasing raw materials.
• Production Management
▫ Facilities planning
 Location and size of warehouse, retail outlets
 Logistics and engineering design
 Transportation planning.
▫ Manufacturing and Facility Planning
 assembly line, blending purchasing and inventory control,
Aggregate production planning
 Maintenance policies.
• Human Resource Management
▫ Manpower planning, salary administration
▫ Scheduling of training programmers to maximize skill development
and retention
▫ Negotiation in a bargaining situation

4. 4
 Personnel Management
▫ Recruitment policies.
▫ Selection a suitable persons
▫ Establishing bonus systems.
Media Selection (Marketing)-
The owner of Big Shop Garment shop is interested to determine how many
advertisements to release in the selected two newspapers ‘A’ Magazine & ‘B’
Magazine .His main purposeis to advertise in such a way that total exposure to
principal buyers of his garments is maximized. Through a survey conducted by the
manufacturer by the businessman, the percentage of principal buyer of his
garments reading the two newspapers is known. Exposure in any particular
newspaper is the number of advertisement released multiplied by the number
principal buyers. The following data are available:
The budgeted amount is at the most Rs. 1.5 lakhs for the advertisements. The
owner has already decided that Times of India should have no more than 15
advertisements and that The Hindu gets no more than 10 advertisements.
Formulate a linear programming model for this problem.
Particulars Newspapers
‘A’ Magazine ‘B’
Magazine
Readers 5 lakh 3 lakh
Principal buyers 30% 25%
Cost per advertisement (in Rs.) 8000 6000

5. 5
Solution:-
Decision variables: Let x1 and x2 be taken as the desired number of insertions in
‘A’ and ‘B’ Magazine respectively.
The total exposure of principal buyers of the newspaper is:
Z= (30% of 500000) x1 + (25% of 300000) x2
Budgeting constraint is:
8000x1 + 6000x2 ≤ 150000
And the advertisements constraints are:
x1 ≤ 15, x2≤10
The appropriate mathematical formulation of the given problem as LP model is:
Maximize (total exposure) Z = 150000x1 + 75000x2
Subject to the constraints
8000x1 + 6000x2 ≤ 150000
0 ≤ x1 ≤ 15
0 ≤ x2 ≤ 10
X1 = 15, x2 = 10 (taken as equation)
X1 x2 = 0 (non - constraints)

6. 6
Graphical Solutions
5 10 15 20 25
25
20
15
10
5
0
18.75
A
B
C D
E
F
x1
x2
x1=15
x2=10
O

7. 7
Region OCDEF is the feasible region. Taking extreme points:
Extreme points (x1,x2) Z=150000x1 + 75000x2
C (0,10) 750000
D (12,10) 2550000
E (15,5) 2625000
F (15,0) 2250000
O (0,0) 0
Interpretation
For point E, Z is Maximum so it is the choice that should be selected. That is,
X1=15 and x2=5
Verifying:
(15 x 8000) + (5 x 6000) = 150000
In this method, the coordinates of all corner points of the feasible region are
determined and then values of the objective function at these points are computed
and compared because the mathematical theory of LP problem always lie at one of
the corner points of the feasible space.

8. 8
Bibliography
1- Kapoor, V. K. (2008) Operations Research (7th Edition), New Delhi, Sultan
Chand & Sons
2- Hillier, F. S., Lieberman, G. J., Nag, B. and Basu, P.(2012) Introduction to
Operations Research (9th Edition), New Delhi, Tata McGraw Hill
3- Natarajan, A.M., Balasubramani, P. And Tamilarasi, A.(2005) Operations
Research, Pearson Publication
4- Sharma, J. K. (2013) Operations Research Theory and Applications(5th
Edition), New Delhi, Macmillan Publishers India Ltd.
5- Taha, H. A. (2012)Operations Research : An Introduction (9th
Edition),Pearson Publication
6- Vohra, N.D (2010). QuantitativeTechniquesin Management (4th Edition),
New Delhi Tata McGraw Hill Publications.
7- Shepard, R.D. Hartley, P. Hasman, L. Thorpe, and M. Bathe, Applied
Operation Research, Plenum Press, New York, 1988.
8- Wagner, H.W. (1975) Principle of Operation Research (2nd Edition)
Prentice Hall, Inc.
9- Swarup, K., Gupta, P.K. and Mohan M. (2012) Introduction to Management
Science: Operation Research (16th Edition) , New Delhi, Sultan Chand and
Sons.