Operation Research

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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

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.

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Purchasing, Procurement and 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

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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 purpose is 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.

Solution:-

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Particulars Newspapers‘A’ Magazine ‘B’

MagazineReaders 5 lakh 3 lakh

Principal buyers 30% 25%Cost per advertisement (in

Rs.)8000 6000

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)

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Graphical Solutions

Region OCDEF is the feasible region. Taking extreme points:

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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

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.

Bibliography

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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). Quantitative Techniques in 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.

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