CONCLUSION ON DEFINITIONS OF OPERATIONS RESEARCH

We read various definitions or opinions about OR,  we arrive at the conclusion that whatever else ' OR ' may be, it is certainly  concerned with optimization problems.    ---- " A decision, which taking  into account all the present circumstances can be considered the best one, is called an optimal decision."

There are three main reasons for why most of the definitions of operation Research are not satisfactory.-------------

1) First of all, Operations research is not a science like any well -defined physical,biological,social phenomena  , while chemists know about atoms and molecules and have theories about their interactions, and biologists know about living organisms and have theories about vital process, operation researchers do not claim to know or have theories about operations.
Operation Research is not a scientific  research into the control of operations. It is essentially a  collection of mathematical techniques and tools which is conjuction with a system approach are applied to solve practical dicision problems of an economic or engineering nature.
Thus it  is very difficult to define operations research precisely.

2) Operation Research is inherently inter-disciplinary in nature with application not only in miitary and business but also in medicine, engineering, physics and so on.  OR make use of experience and expertise of people from different disciplines for developing new methods and procedures.
              Thus inter-disciplinary approach is an important characteristic of OR, which is not included in most of its definitions.
Hence most of definitions are  not satisfactory.

3) Most of the definitions of OR have been offered at different times of  development of OR and hence are bound to emphasise its only one or the other aspect.
For example---- some definitions is only  concerned with war alone.
Many more definitions have been given by various authors must of them fail to consider all basic characteristic of OR ..

However, with further development of operation research perhaps more precise definitions should be forthcoming.

Management Applications of operations research

Some of the areas of management decision making, where the "tools" and " techniques" of OR are applied, can be outlined as follows :

1) Finance-Budgeting and Investments
(1) Cash-flow analysis, long rang capital requirements, dividend policies, investment portfolios.
(2) credit policies, credit risks and delinquent account procedures.
(3) Claim and complaint procedures

2) Purchasing,  Procurement and Exploration
(1) Rules for buying, Supplies and stable or varying prices.
(2) Determination of quantities and timing of purchase
(3) Bidding policies
(4) Strategies for exploration and exploitation of raw material sources
(5) Replacement policies

3. Production Management

(1) Physical Distribution
       (a) Location and size of warehouse, distribution centres and retail  sources.
       (b) Distribution  policy

(2) Facilities planning
       (a) Numbers and location of factories, warehouse, hospitals  etc.
       (b) Loading and unloading facilities for railroads and trucks determine the transport schedule.

(3) Manufacturing
     (a) Production scheduling and sequencing
     (b) Stabilization of production and employment, training, layoffs and optimum product mix.

(4) Maintenance and Project Scheduling
       (a) Maintenance policies and preventive maintance.
       (b) Maintence crew sizes.
       (c) Project scheduling and allocation of resources.

4. Marketing
     (a) Product selection, timing competitive actions.
     (b) Number of salesman, frequency of calling an accounts percent of time spent on prospects
    (c) Advertising  media with respect to cost  and time.

5. Personnel Management
    (a) Selection of suitable personnel on minimum salary
    (b) Mixes of age and skills
    (c) Recruitment policies and assignment of jobs.

6. Research and Development
     (a) Determination of  the areas of concentration of research and development
    (b) Project selection
    (c) Determination of time cost trade-off and control of development  projects
    (d) Reliability and alternative desine.

THE NATURE AND MEANING OF " OPERATION RESEARCH" - "OR"

'OR' has been defined so far in various ways and it is perhaps still too yaung to be defined in some  authoritative way. So it is importent and interesting to give below a few opinions about the definition of OR which has been changed according to development of the subject. -----

1. OR is a scientific method of providing executive with an  analytical and objective basis  for decisions.             ---  P.M.S. Blackett (1948)

2. OR is the art of giving bad answers to problems to which otherwise worse answers are given.     ---- T.L. Saaty (1958)

3. OR is the application of scientific methods , techniques, and tools to problems involving the operations of systems so as to provide these in control of the operations with optimum solutions to the problem. 
                    ---- Churchman,Acorff,Arnoff (1957)

4. OR is a management activity pursued in two complementary ways --- one half by the free and bold exercise of commonsense untrammelled by any routine,  and other half by the application of a repertoire of well established precreated methods and techniques .
                     --- Jagjit Singh (1958)

5. OR is the  attack of modern methods on complex problems arising in the direction and management to large system of men, machines, materials, and money in industry, business and defence. The distinctive approach is to developed a scientific model of the system, incorporating measurements of factors such as chance and risk with which to predict and compare the outcomes of alternative decisions, strategies or controls. The purpose is to help management to determine its policy and actions scientifically.

                            ---  Operations Research Quarterly (1971)

6. OR is a scientific approach to  problem solving fo executive management.
                    --- H.M. Wagner
7. Operation research is the art of wining war without actually fighting it.

Analytic Functions

A complex function is said to be analytic on a region R,  if it is differentiable at every point in R.
The terms " Holomorphic function " are also used for analytic function.

If a complex function is analytic on a region R, it is infinitely differentiable in R. A complex function may fail to be analytic at one or more point through the presence of singularities.

" A complex function that is analytic at all finite points of the complex plane is said to be entire function ."

A single valued function that is analytic in,  all but possibly a discrete subset of its  domain, and at those singularities goes to infinity like a polynomial is called a meromorphic function.

Maths puzzal

See the photo below and give answer :

RELIABILITY THEORY

Reliability theory is a new scientific discipline that studies the general regularity that must be maintained under, experimentation , manufacture, acceptance, and  use of units in order to obtain high system effectiveness form their use.
Reliability is determind by quality and operating characteristics. The problem of increasing reliability of units is becoming ever more important and urgent in connection with the complex mechanisation and automation of industrial processes in many field of industry, transport, communication,  technology etc..

Availability of maths in various courses

Mathematics is the commen subject to all major courses  ,viz B.sc, BCA  ,B.Tech. ,B.pharma. , Polytechnic ( diploma in engg. ) , M.sc  , M.tech. M.phill. ,Economics, Statistics,  etc.
The study of maths is necessary in all above course.