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B.E./B.Tech. DEGREE EXAMINATION

(Regulation/Scheme 2010)

10IS661/10CS661 Operations Research

10IS661/10CS661 Operations Research

Sixth Semester - 6th

Computer Science Engineering - CSE

(Common to Information Science Engineering)

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**Question Paper Solution**

UNIT-1

UNIT-1

Q1 Explain the limitations of OR model. (DEC-2010)

Solution: LIMITATIONS OF OR

1) Mathematical models with are essence of OR do not take into account qualitative

factors or Emotional factors.

2) Mathematical models are applicable to only specific categories of problems

3) Being a new field, there is a resistance from the employees the new proposals.

4) Management may offer a lot of resistance due to conventional thinking.

5) OR is meant for men not that man is meant for it.

Difficulties of OR

1) The problem formulation phase

2) Data collection

3) Operations analyst is based on his observation in the past

4) Observations can never be more than a sample of the whole

5) Good solution to the problem at right time may be much more useful than perfect

solutions

Q2. A company has two grades of inspectors, 1 and 2 to undertake quality control

inspection. At least 1,500 pieces must be inspected in an 8 hour day. Grade 1

inspector can check 20 pieces in an hour With an accuracy of 96%. Grade 2

inspector checks 14 pieces an hour with an accuracy of 92%.The daily wages of

grade 1 inspector are Rs. 5 per hour while those of grade inspector are Rs. 4 per

hour, any error made by an inspector costs Rs. 3 to the company. If there are, in all,

10 grade 1Inspectors and 15 grade 2 inspectors in the company, find the optimal

assignment of inspectors that Minimize the daily inspection cost.

(DEC 2010)

Solution

Let x1, x2 be the inspector of grade 1 and 2.

Grade 1: 5 + 3 * 0.04 * 20

Grade 2: 4 + 3 * 0.08 * 14

Z = 8*(7.4x1 + 7.36x2)

X1 =10, x2 =15

20 * 8 x1 + 14* 8 x2 =1500

Q3. List the steps conducting in operational research study (JUNE 2011)

Solution: steps of OR

1) Formulating the problem

In formulating a problem for OR study, we mist be made of the four major components.

i) The environment

ii) The decision maker

iii) The objectives

iv) Alternative course of action and constraints

2) Construction a Model

After formulating the problem, the next step is to construct mode. The mathematical

model consists of equation which describes the problem.the equation represent

i) Effectiveness function or objective functions

ii) Constraints or restrictions

The objective function and constraints are functions of two types of variable, controllable

variable and uncontrollable variable.

A medium-size linear programming model with 50 decision variable and 25 constraints

will have over 1300 data elements which must be defined.

3) Deriving solution from the model

An optimum solution from a model consists of two types of procedure: analytic and

numerical. Analytic procedures make use of two types the various branches of

mathematics such as calculus or matrix algebra. Numerical procedure consists of trying

various values of controllable variable in the mode, comparing the results obtained and

selecting that set of values of these variables which gives the best solution.

4) Testing the model

a model is never a perfect representation of reality. But if properly formulated and

correctly manipulated, it may be useful predicting the effect of changes in control

variable on the overall system.

5) Establishing controls over solution

a solution derived from a model remains a solution only so long as the uncontrolled

variable retain their values and the relationship between the variable does not change.

6) Implementation

OR is not merely to produce report to improve the system performance, the result of the

research must implement. Additional changes or modification to be made on the part of

OR group because many time solutions which look feasible on paper may conflict with

the capabilities and ideas of persons.

Q4.Briefly explain the scopes of OR. (JUNE 2010)

SOLUTION:

Scope of Operation Research

1) Industrial management:

a) Production b) product mix c) inventory control d) demand e) sale and purchase f)

transportation g) Repair and maintenance h) scheduling and control

2) Defense operations:

a) Army b) air force c) navy

All these further divided into sub-activity, that is, operation, intelligence administration,

training.

3) Economies:

Maximum growth of per capita income in the shortest possible time, by taking into

consideration the

National goals and restrictions impose by the country. The basic problem in most of the

countries is

to remove poverty and hunger as quickly as possible.

4) Agriculture section:

a) With population explosion and consequence shortage of food, every country is facing

the problem Of optimum allocation land to various crops in accordance with climatic

conditions.

b) Optimal distribution of water from the various water resources.

5) Other areas:

a) Hospital b) transport c) LIC

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