• Operations research, or operational research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions. It is often considered to be a sub-field of mathematics. The terms management science and decision science are sometimes used as more modern-sounding synonyms.

• Employing techniques from other mathematical sciences, such as mathematical modelling, statistical analysis, and mathematical optimization, operations research arrives at optimal or near-optimal solutions to complex decision-making problems. Because of its emphasis on human-technology interaction and because of its focus on practical applications, operations research has overlap with other disciplines, notably industrial engineering and operations management, and draws on psychology and organization sciences. Operations Research is often concerned with determining the maximum(of profit, performance, or yield) or minimum (of loss, risk, or cost) of some real-world objective. Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries.

According to Philip McCord Morse and George E. Kimball,"Operations research is a scientific method of providing executive departments with a

quantitative basis for decisions regarding the operations under their control.“ According to Russell L. Ackoff and C. West Churchman,"Operations research is the application of scientific methods to arrive at the optimal

solutions to the problems.“ O.R. is the art of winning wars without actually fighting. - Arthur Clarke O.R. is concerned with scientifically deciding how to best design and operate man-

machine systems usually under conditions requiring the allocation of scarce resources. -O.R. Society of America

O.R. is the art of giving bad answers to problems which otherwise have worse answers. -T.L. Saaty

O.R. is applied decision theory. It uses any scientific, mathematical or logical means to attempt to cope with the problems that confront the executive, when he tries to achieve a thorough-going rationality in dealing with his decision problems. -D.W. Miller and M.K. Starr

O.R. is a scientific approach to problems solving for executive management. -H.M. Wagner

O.R. is the study of administrative system pursued in the same scientific manner in which systems in Physics, Chemistry and Biology are studied in natural sciences.

Systems Orientation - This approach recognizes the fact that the behaviour of any part of the system has an effect on the system as a whole. This stresses the idea that the interaction between parts of the system is what determines the functioning of the system. No single part of the system can have a bearing effect on the whole. OR attempts appraise the effect the changes of any single part would have on the performance of the system as a whole.

Interdisciplinary groups - The team performing the operational research is drawn from different disciplines. The disciplines could include mathematics, psychology, statistics, physics, economics and engineering. The knowledge of all the people involved aids the research and preparation of the scientific model.

Provides Quantitative Answers - The solutions found by using operations research are always quantitative. OR considers two or more options and emphasizes the best one. The company must decide which option is the best alternative for it.

Human Factors - In other forms of quantitative research, human factors are not considered, but in OR, human factors are a prime consideration. People involved in the process may become sick, which would affect the company's output.

Operations research (OR) is a management function that draws extensively from the divisions of mathematics and science. It makes use of algorithms, statistics and numerous modelling techniques from mathematics to find the best possible solutions for complex problems. In OR, the maxima has to be optimized and the minima has to be reduced for all the objects involved. Maxima are usually the yield, performance and profit and minima are the losses and risks. There are many reasons to use OR.

Business Operations - OR could be very effective in handling issues of inventory planning and scheduling, production planning, transportation, financial and revenue management and risk management. Basically, OR could be used in any situation where improvements in the productivity of the business are of paramount importance.

Control - With OR, organizations are greatly relieved from the burden of supervision of all the routine and mundane tasks. The problem areas are identified analytically and quantitatively. Tasks such as scheduling and replenishment of inventories benefit immensely from OR.

Decision Making - OR is used for analysing problems of decision making in a superior fashion. The organization can decide on factors such as sequencing of jobs, production scheduling and replacements. Also the organization can take a call on whether or not to introduce new products or open new factories on the basis of a good OR plan.

Coordination - Various departments in the organization can be coordinated well with suitable OR. This facilitates smooth functioning for the entire organization.

Systems - With OR, any organization follows a systematic approach for the conduct of its business. OR essentially emphasizes the use of computers in decision making; hence the chances of errors are minimum.

• Linear Programming. Linear Programming (LP) is a mathematical technique of assigning a fixed amount of resources to satisfy a number of demands in such a way that some objective is optimized and other defined conditions are also satisfied.

• Transportation Problem. The transportation problem is a special type of linear programming problem, where the objective is to minimize the cost of distributing a product from a number of sources to a number of destinations.

• Assignment Problem. Succinctly, when the problem involves the allocation of n different facilities to n different tasks, it is often termed as an assignment problem.

• Queuing Theory. The queuing problem is identified by the presence of a group of customers who arrive randomly to receive some service. This theory helps in calculating the expected number of people in the queue, expected waiting time in the queue, expected idle time for the server, etc. Thus, this theory can be applied in such situations where decisions have to be taken to minimize the extent and duration of the queue with minimum investment cost.

• Game Theory. It is used for decision making under conflicting situations where there are one or more opponents (i.e., players). In the game theory, we consider two or more persons with different objectives, each of whose actions influence the outcomes of the game. The game theory provides solutions to such games, assuming that each of the players wants to maximize his profits and minimize his losses.

• Inventory Control Models. It is concerned with the acquisition, storage, handling of inventories so as to ensure the availability of inventory whenever needed and minimize wastage and losses. It help managers to decide reordering time, reordering level and optimal ordering quantity.

• Goal Programming. It is a powerful tool to tackle multiple and incompatible goals of an enterprise. • Simulation. It is a technique that involves setting up a model of real situation and then performing

experiments. Simulation is used where it is very risky, cumbersome, or time consuming to conduct real study or experiment to know more about a situation.

• Nonlinear Programming . These methods may be used when either the objective function or some of the constraints are not linear in nature. Non-Linearity may be introduced by factors such as discount on price of purchase of large quantities.

• Integer Programming . These methods may be used when one or more of the variables can take only integral values. Examples are the number of trucks in a fleet, the number of generators in a power house, etc.

• Dynamic Programming. Dynamic programming is a methodology useful for solving problems that involve taking decisions over several stages in a sequence. One thing common to all problems in this category is that current decisions influence both present & future periods.

• Sequencing Theory. It is related to Waiting Line Theory. It is applicable when the facilities are fixed, but the order of servicing may be controlled. The scheduling of service or sequencing of jobs is done to minimize the relevant costs. For example, patients waiting for a series of tests in a hospital, aircrafts waiting for landing clearances, etc.

• Replacement Models. These models are concerned with the problem of replacement of machines, individuals, capital assets, etc. due to their deteriorating efficiency, failure, or breakdown.

• Markov Process . This process is used in situations where various states are defined and the system moves from one state to another on a probability basis. The probability of going from one state to another is known. This theory helps in calculating long run probability of being in a particular state.

• Network Scheduling-PERT and CPM. Network scheduling is a technique used for planning, scheduling and monitoring large projects. Such large projects are very common in the field of construction, maintenance, computer system installation, research and development design, etc. Projects under network analysis are broken down into individual tasks, which are arranged in a logical sequence by deciding as to which activities should be performed simultaneously and which others sequentially.

• Symbolic Logic. It deals with substituting symbols for words, classes of things, or functional systems. It incorporates rules, algebra of logic, and propositions. There have been only limited attempts to apply this technique to business problems; however, it is extensively used in designing computing machinery.

• Information Theory. It is an analytical process transferred from the electrical communications field to operations research. It seeks to evaluate the effectiveness of information flow within a given system and helps in improving the communication flow.

1. Mathematical models (viz. linear programming formulation of the blending problem or transportation problem) are the most abstract type since it requires not only mathematical knowledge but also great concentration :o get .he idea of the real-life situation they represent. 16

2. Language models (cricket or hockey match commentary) are also abstract type. Concrete models (model of earth, dam, building or plane) are the least abstract since they instantaneously suggest the shape or characteristics of the modelled entity.

3. Descriptive models explain the various operations in non-mathematical language and try to define the functional relationships and interactions between various operations. They simply describe some aspects of the system on the basis of observation, survey or questionnaire, etc. but do not predict its behaviour. The organisational chart, pie diagram and layout plan describe the features of their respective systems.

4. Predictive models explain or predict the behaviour of the system. Exponential smoothing forecast model, for instance, predicts the future demand.

5. Normative or prescriptive models develop decision rules or criteria for optimal solutions. They are applicable to repetitive problems, the solution process of which can be programmed without managerial involvement. Linear programming is a prescriptive or normative model as it prescribes what the managers must follow.

6. Iconic or Physical Models - In iconic or physical models, properties of the real system are represented by the properties themselves, frequently with a change of scale. Thus, iconic models resemble the system they represent but differ in size; they are images. For example, globes are used to represent the orientation and shape or various continents, oceans and other geographical features of the earth. A model of the solar system, likewise, represents the sun and planets in space. Iconic models of atoms and molecules are commonly used in physics, chemistry and other sciences.

7. Analogue or Schematic Models - Analogue models can represent dynamic situations and are used more often than iconic models since they are analogous to the characteristics of the system under study. They use one set of properties to represent some other set of properties which the system under study possesses. After the model is solved, the solution is re-interpreted in terms of the original system.

o For example, graphs are very simple analogues. They represent properties like force, speed age, time, etc., in terms of distance. A graph is well suited for representing quantitative relationship between any two properties and predicts how a change in one property affects the other.

o An organizational chart is a common schematic model. It represents the relationships existing between the various members of the organization.

8. Probabilistic Modelso They are the products of an environment of risk and uncertainty. The input and/or output

variables take the form of probability distributions. They are semi-closed models and represent

o the likelihood of occurrence of an event. Thus they represent, to an extent, the complexity of the real world and the uncertainty prevailing in it. As an example, the exponential smoothing model for forecasting demand is a probabilistic model.

9. Symbolic or Mathematical Models - Symbolic models employ a set of mathematical symbols (letters, numbers, etc.) to represent the decision variables of the system under study. These variables are related together by mathematical equation(s)/inequation(s) which describe the properties of the system. A solution from the model is, then, obtained by applying well developed mathematical techniques. The relationship between velocity, acceleration and distance is an example of mathematical model. Similarly, cost-volume-profit relation is a mathematical model used in investment analysis. In many research projects, all the three types of models are used in sequence; iconic and analogue models are used as initial approximations, which are, then, refined into symbolic model. Mathematical models differ from those traditionally used in physical sciences in two ways:

a) Since OR systems involve social and economic factors, these models use probabilistic elements.

b) They consist of two types of variables; controllable and uncontrollable. o The objective is to select those values for controllable variables which optimize some

measure of effectiveness. Therefore, these models are used in decision situations rather than in physical phenomena.

o In OR, symbolic models are used wherever possible, not only because they are easier to manipulate but also because they yield more accurate results. Most of this text, therefore, is devoted to the formulation and solution of these mathematical models.

10. Deterministic Models - In deterministic models variables are completely defined and the outcomes are certain. Certainty is the state of nature assumed in these models. They represent completely closed systems and the parameters of the system have a single value that does not change with time. For any given set of input variables, the same output variables always result . EOQ model is deterministic; here the effect of changes in the batch sizes on the total cost is known. Similarly linear programming, transportation and assignment models are deterministic models.

• Having-known-the definition of OR, it is easy to visualize the scope of operations research. When we broaden the scope of OR, we find that it has really been practised for hundreds of years even before World War II. Whenever there is a problem of optimization, there is scope for the application of OR. Its techniques have been used in a wide range of situations:

• 1. In Industry • In the field of industrial management, there is of chain of problems starting from the purchase of raw materials to the

dispatch of finished goods. The management is interested in having an overall view of the method of optimizing profits. OR study should also point out the possible changes in the overall structure like installation of a new machine, introduction of more automation, etc. OR has been successfully applied in industry in the fields of production, blending, product mix, inventory control, demand forecast, sale and purchase, 10

• transportation, repair and maintenance, scheduling and sequencing, planning, scheduling and control of projects and scores of other associated areas.

• 2. In Defence • OR has a wide scope for application in defence operations. In modern warfare the defence operations are carried out by a

number of different agencies, namely airforce, army and navy. The activities performed by each of them can be further divided into sub-activities viz. operations, intelligence, administration, training and the like. There is thus a need to coordinate the various activities involved in order to arrive at optimum strategy and to achieve consistent goals. Operations research, conducted by team of experts from all the associated fields, can be quite helpful to achieve the desired results.

• 3. Planning • In both developing and developed economies, OR approach is equally applicable. In developing economies, there is a great

scope of developing an OR approach towards planning. The basic problem is to orient the planning so that there is maximum growth of per capita income in the shortest possible time, by taking into consideration the national goals and restrictions imposed by the country. The basic problem in most of the countries in Asia and Africa is to remove poverty and hunger as quickly as possible. There is, therefore, a great scope for economists, statisticians, administrators, technicians, politicians and agriculture experts working together to solve this problem with an OR approach.

• 4. Agriculture • OR approach needs to be equally developed in agriculture sector on national or

international basis. With population explosion and consequent shortage of food, every country is facing- the problem of optimum allocation of land to various crops in accordance with climatic conditions and available facilities. The problem of optimal distribution of water from the various water resources is faced by each.

• developing country and a good amount of scientific work can be done in this direction. • 5. Public Utilities • OR methods can also be applied in big hospitals to reduce waiting time of out-door

patients and to solve the administrative problems, • Monte Carlo methods can be applied in the area of transport to regulate train arrivals and

their running times. Queuing theory can be applied to minimize congestion and passengers' waiting time.

• OR is directly applicable to business and society. For instance, it is increasingly being applied in LIC offices to decide the premium rates of various policies. It has also been extensively used in petroleum, paper, chemical, metal processing, aircraft, rubber, transport and distribution, mining and textile industries.

• OR approach is equally applicable to big and small organizations. For example, whenever a departmental store faces a problem like employing additional sales girls, purchasing an additional van, etc., techniques of OR can be applied to minimize cost and maximize benefit for each such decision.

• Thus we find that OR has a diversified and wide scope in the social, economic and industrial problems of today.

Practical Application – O.R. provides solution when all the elements related to a problem can be quantified. Hence various intangible factors such as working conditions, human relations remain excluded which may be of more significance than quantified factors.

Costly Operations – O.R. techniques are usually very expensive as they require services of specialized persons and computers.

Reliability of the proposed solution – Sometimes a non – linear relationship is changed to linear for fitting the problem to L.P. pattern. In such cases, the result may be incorrect.

Competence – Competent O.R. analysis needs careful speculation of alternatives, a full comprehension of the underlying mathematical relationships and a huge mass of data. Formulation of an industrial problem to an O.R. set programme is not easy task.

• Dependence on an Electronic Computer: O.R. techniques try to find out an optimal solution taking into account all the factors. In the modern society, these factors are enormous and expressing them in quantity and establishing relationships among these require voluminous calculations that can only be handled by computers.

• Non-Quantifiable Factors: O.R. techniques provide a solution only when all the elements related to a problem can be quantified. All relevant variables do not lend themselves to quantification. Factors that cannot be quantified find no place in O.R. models.

• Distance between Manager and Operations Researcher: O.R. being specialist's job requires a mathematician or a statistician, who might not be aware of the business problems. Similarly, a manager fails to understand the complex working of O.R. Thus, there is a gap between the two.

• Money and Time Costs: When the basic data are subjected to frequent changes, incorporating them into the O.R. models is a costly affair. Moreover, a fairly good solution at present may be more desirable than a perfect O.R. solution available after sometime.

• Implementation: Implementation of decisions is a delicate task. It must take into account the complexities of human relations and behaviour.