Here is a compilation of essays on ‘Operation Research’ for class 11 and 12. Find paragraphs, long and short essays on ‘Operation Research’ especially written for college students.
Essay on Operation Research
Essay Contents:
- Essay on the Introduction to Operation Research
- Essay on the Definition of Operation Research
- Essay on the Development of Operation Research
- Essay on the Characteristics of Operation Research
- Essay on the Scope of Operation Research
- Essay on the Models in Operation Research
- Essay on the Problem Formulation in Operations Research
- Essay on the Role of Computer in Operation Research
Essay # 1. Introduction to Operation Research:
Now-a- days life is becoming more and more complex. One has to take certain decision for himself and for others. A student has to decide which course he should take for study. A person seeking employment has to decide which job he should choose for service.
ADVERTISEMENTS:
Therefore, one has to develop his talent in such a way that he is in a position to take a correct decision at a proper time. An effective decision depends on many factors which may be economic, social & political.
Therefore, understanding of the possible use of scientific approach in decision-making is of great importance to the business students. Operation research provides a quantitative technique or a scientific approach to the executives for making better decisions for operation under their control.
Figure 4.1 A conceptual framework of a possible structural analysis of or application process in an organisation.
Figure 4.1 summarizes the operation research approach by sketching the conceptual framework of the main elements of the analysis.
ADVERTISEMENTS:
Operation Research is assuming an increasing degree of importance in theory and practice of management.
Some of the factors which are responsible for this development are:
(1) Decision problems of modern management are so complex that only a systematic and scientifically based analysis can yield realistic solutions.
ADVERTISEMENTS:
(2) Availability of different types of quantitative models for solving these complex managerial problems.
(3) Availability of high-speed computers has made it possible both in terms of time and cost to apply quantitative models to all real-life problems in all types of organisations such as business and industry.
Essay # 2. Definition of Operation Research:
Operations research, rather simply defined, is the research of operations. An operation may be called a set of acts required for the achievement of a desired outcome.
ADVERTISEMENTS:
According to Morse and Kimball, “OR is a scientific method of providing executive department with a quantitative basis for decisions regarding the operations under their control.”
According to churchman, Ackoff and Arnoff:
“OR in the most general sense, can be characterised as the application of scientific methods, tools and techniques to problems involving the operations of systems so as to provide those in control of the operations with optimum solutions to the problems.”
Essay # 3. Development of Operation Research:
i. Pre-World War II:
ADVERTISEMENTS:
No science has ever been bark on a specific day, operation research is no exception. Its roots are as old as science though the roots of OR extend to even early 1800s, it was in 1885 when Frederick W. Taylor emphasised the application of scientific analysis to methods of production, that the real start took place.
Taylor conducted experiments in connection with a simple shovel. His aim was to find that weight load of ore moved by shovel which would result in maximum of ore moved with minimum of fatigue. After many experiments with varying weight, he obtained the optimum weight load, which though much lighter than that commonly used, provided maximum movement of ore during a day.
Another man of early scientific management era was Henry L. Gault. Most job-scheduling methods at that time were rather haphazard. A job, for instance, may be processed on a machine without trouble but then wait for day for acceptance by the next machine. Gault mapped each job from machine to machine, minimizing every delay. Now with the Gault procedure it is possible to plan machine loading months in advance and still quote delivery dates accurately.
In 1917. A.K. Erlang, a Danish mathematician, published his work on the problem of congestion of telephone traffic.
The well-known economic lot size model is attributed to F.W. Harris, who published his work on the area of inventory control in 1915.
During the 1930s, H.C. Levinson. an American astronomer, applied scientific analysis to the problems of merchandising.
However, it was the first Industrial Revolution which contributed mainly towards the development of OR.
ii. World War II:
During World War II, the military management in England called on a team of scientists to study the strategic and tactical problems of air and land defence. This team was under the direction of Professors P.M.S. Blackett of univo of Manchester and a former naval officer.
The objective was to find out the most effective allocation of limited military resources to the various military operations and to the activities within each operation. The application included the effective use of newly invented radar, allocation of British Air Force Planes to missions and the determination of best patterns for searching submarines. The group of scientists formed the first OR team.
The name operations research was apparently coined because the team was carrying out research on operations. In United States these OR teams helped in developing strategies for mining operations, inventing new flight patterns and planning of sea mines.
iii. Post- World War II:
Immediately after the war, the success of military teams attracted the attention of industrial managers who were seeking solution to their problems. Industrial operations research in U.K. and U.S.A. developed along different lines. In U.K., the critical economic situations, required drastic increase in production efficiency and creation of new markets. Nationalisation of a few key industries further increased the potential field for OR.
In U.S.A the situation was different, impressed by its dramatic success in U.K., defence Most of the war experienced OR workers remained in Military services. The progress of industrial operation research in U.S.A was due to advent of second industrial revolution which resulted in automation the replacement of man by machine as a source of control.
The new revolution began around 1940s when electronic computers became commercially available. These electronic brains possessed tremendous computational speed and information storage.
In 1950, OR was introduced as a subject for academic study in American universities. Since this subject has been gaining ever increasing importance for the students of Mathematics, Statistics, Commerce, Economics, Management and Engineering. To increase the impact of operations research, the Operations Research Society of America was formed in 1950.
Today, the impact of OR can be felt in many areas.
Operations Research in India:
In India, OR came into existence with the opening of an OR unit in 1949 at the Regional Research Laboratory at Hyderabad. An OR unit under professor P.C. Mahalonobis was established in 1953 in the Indian Statistical Institute, Calcutta to apply OR methods in national planning and survey.
Operation Research Society of India was formed in 1957 and its first conference was held in Delhi in 1959. It was felt that there existed the need of producing well-trained operations researchers who could tackle practical problem. It was also decided to bring out a journal on operations research, the first volume of which came out in 1963 with the name of “Opsearch”.
Professor Mahalonobis made the first important application of OR in India in preparing the draft of the second five year plan. For academic studies, the first M.Sc. course on OR was started by Delhi University in 1963. At the same time. Institute of Management at Calcutta and Ahmedabad introduced OR in their MBA courses. At present, this subject has been introduced in all Institutes and universities for the students.
A number of organisations are utilizing OR techniques of solving problems relating to staffing, production planning, blending, product mix. maintenance inspection, advertising, capital budgeting, investment and the like.
Essay # 4. Characteristics of Operation Research:
The essential characteristics of operation research are:
i. System Orientation of OR:
The term systems approach implies that each problem should be examined in its entirety to the extent possible and economically feasible from the point of view of the overall system of which the problem under consideration is one part. Under this approach a manager makes conscious attempt to understand the relationships among various parts of the organisation and their role in supporting the overall performance of the organisation.
In other words “Operation Research is the scientific study of large systems with a view to identify problem areas and provide the managers with a quantitative basis for decisions which will enhance their effectiveness in achieving the specified objectives”.
ii. The use of Interdisciplinary Teams:
The second characteristic of OR is that it is performed by a team of scientists whose individual members have been drawn from different scientific and engineering disciplines.
It has been recognised beyond doubt that people from different disciplines can produce more unique solutions with greater probability of success, than could be expected from the same member of persons from a single discipline. Thus the OR team can look at the problem from many different angles in order to determine which one of approaches is the best.
iii. Application of Scientific Method:
The third distinguishing feature of OR is the use of scientific method to solve the problem under study. Specially, the process begins with the careful observation and formulation of the problem. The next step is to construct a scientific model that attempts to abstract the essence of the real problem.
iv. Uncovering of New Problems:
The fourth characteristic of OR, which is often overlooked, is that solution of an OR problem may uncover a number of new problem. Of course, all the uncovered problems need not be solved at the same time. However, in order to derive maximum benefit, each one of them must be solved. It must be remembered that OR is not effectively used if it is restricted to one-short problems only. In order to derive full benefits, continuity of research must be maintained.
v. Improvement in the Quality of Decisions:
OR gives bad answer to problems, to which, otherwise, worse answers are given. It implies that by applying its scientific approach, it can only improve that quality of solution but it may not be able to give perfect solution.
vi. Use of Computer:
Another characteristics of OR is that it often requires a computer to solve the complex mathematical model or to manipulate a large amount of data or to perform a large number of computations that are involved.
vii. Quantitative Solutions:
OR approach provides the management with a quantitative basis for decision-making.
viii. Human Factors:
In deriving quantitative solutions we do not consider human factors, which doubtlessly play a great role in the problems posed. Definitely an OR study is incomplete without a study of human factors.
Essay # 5. Scope of Operations Research:
By the definition of OR, it is clearly understood the scope of Operation Research whenever there is a problem for optimization, there is scope for the application of OR.
Some of the areas of Management where techniques of OR are applied are listed below:
i. Finance, Budgeting and Investments:
(a) Cash flow analysis, investment portfolios.
(b) Credit policies, credit risks.
(c) Claim and complaint procedures.
ii. Purchasing, Procurement and Explorations:
(a) Determining the quantity and timing of purchase of raw material.
(b) Bidding policies.
(c) Equipment replacement policies.
iii. Production Management:
(a) Project planning.
(b) Manufacturing and facility planning.
iv. Marketing Management:
(a) Product selection, timing & competitive action.
(b) Advertising strategy.
(c) Effectiveness of market research.
v. Personnel Management:
(a) Recruitment policies and assignment of jobs.
(b) Selection of suitable personnel.
(c) Establishing equitable bonus systems.
vi. Research and Development:
(a) Determination areas of concentration of research and development.
(b) Reliability and evaluation of attractive design.
(c) Control of development Project.
From all above areas of application, it is clear that OR can be widely used in taking timely management decisions and also used as a corrective measure.
Essay # 6. Models in Operation Research:
A model, as used in operation research, is defined as an idealized representation of the real life situation it represents one or a few aspects of reality. Diverse items such as a map, a multiple activity chart, an autobiography, PERT network, break even equation, balance sheet etc. are all models because each one of them represents a few aspects of the real-life situation. The objective of the model is to provide a means for analyzing the behaviour of the system for the purpose of improving its performance.
Classification of Operation Research Models:
The various schemes by which models can be classified are given below:
i. By degree of Abstraction:
Mathematical models are the most abstract type since it requires not only mathematical knowledge but also great concentration to get the idea of the real-life situation they represent. Language models are also abstract type like cricket or hockey match commentary and concrete models (model of earth, dam) are the least abstract since they instantaneously suggest the shape.
ii. By function:
Descriptive models explain the various operations in non-mathematical language and try to define the functional relationships and interactions between various operations. The organizational chart, pie diagram and layout plan describes the features of their respective system. Predictive models explains or predict the behaviour of the system. Normative models develop decision rules or criteria for optimal solutions.
iii. By structure:
(a) 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.
(b) 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.
(c) Symbolic or Mathematical Models:
Symbolic models employ a set of mathematical symbols to represent the decision variables of the system under study. These variables are related together by mathematical equation/ in equation, which describe the properties of the system. 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.
iv. By Nature of the Environment:
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 results are single valued.
Probabilistic Models:
They are the product 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 the likelihood of occurrence of an event.
v. By the Extent of Generality:
(a) General Models:
Linear programming model is known as a general model since it can be used for all the functions of an organisation.
(b) Specific Models:
Sales response curve or equation as a function of advertising is applicable in the marketing function alone.
(6) By the time Horizon:
(a) Static Models:
They are one-time decision models. In these models cause and effect occur almost simultaneously and time lag between the two is zero. They are easier to formulate, manipulate and solve.
(b) Dynamic Models:
They are the models for situations in which time often play an important role. They are used for optimization of multistage decision problems which require a series of decisions with the outcome of each depending upon the results of the previous decisions in the series.
Characteristics of a Good Model:
(1) The number of simplifying assumptions should be as few as possible.
(2) The number of relevant variables should be as few as possible. This means model should be simple yet close to reality.
(3) It should assimilate the system environmental changes without change in its framework.
(4) It should be adaptable to parametric type of treatment.
(5) It should be easy and economical to construct.
Advantages of a Model:
(1) It provides a logical and systematic approach to the problem.
(2) It indicates the scope as well as limitations of a problem.
(3) It helps in finding avenues for new research and improvements in a system.
(4) It makes the overall structure of the problem more comprehensive and helps in dealing with the problem in its entirely.
Limitations of a Model:
(1) Models are only idealized representation of reality and not be regarded as absolute in any case.
(2) The validity of a model for a particular situation can be ascertained only by conducting experiments on it.
Essay # 7. Problem Formulation in Operations Research:
While both recognition and formulation of LP problems tend to become intuitive after we gain experience, in the beginning a method to follow helps us to more effectively formulate them.
A two-phase procedure can be employed in formulating a problem:
(1) Verbalize the problem and its structure.
(2) Develop the mathematical structure.
Expressed more explicitly, the following steps should be employed:
Phase 1:
(a) Provide a detailed verbal description of the problem under consideration, ensuring that related information is unambiguous and sufficiently precise. It is essential that we have a clear and adequate understanding of the problem under investigation before we seek to apply the technique itself.
(b) Determine the overall objective that appears to be relevant. It will usually be clear whether the objective relates to some maximization or minimization, to cost or profit and so on.
(c) Determine the factors (Constraints) that appear to restrict in some way the attainment of the objective identified in the previous stage. These stages together will provide a detailed verbal exposition of the complete problem under investigation.
Phase 2:
Once the problem has been described verbally, the next step is transform the verbal descriptions into the proper mathematical structure.
A workable procedure to employ at this stage of the problem formulation process is as follows:
(a) Define the decision variables that are relevant to the problem and as is often important, ensure that this units of measurement are explicitly stated. Failure to do so may well lead to difficulty in formulating appropriate constraints and in interpreting the solution results.
(b) Identify the contribution coefficients associated with each variable;
(c) Formulate the objective function quantitatively and experimentally and express it is a linear function of decision variables.
(d) Identify the physical rate of substitution coefficients (the aij‘s)
(e) Identify the available resources or requirements, i.e., the right-hand-side coefficients (the bi‘s).
(f) Formulate suitable mathematical constraints related to each respective resource or requirement as linear equalities/inequalities in terms of decision variables.
(g) Mention the non-negativity condition associated with the decision variables.
Essay # 8. Role of Computer in Operation Research:
Recent developments in the field of computer technology have enabled Operations Research to integrate their models into information systems and thus make O.R. a part of decision – making procedures of many organisations.
Use of a digital computer has become an integral part of the O.R approach in decision making. The computer may be required due to the complexity of the model, volume of data required or the computations to be made. In other words, computer in today’s scenarios has become an indispensable tool for solving Operations Research problems. Many O.R. techniques are available today in the form of ‘canned’-programmes.
The O.R. problems are time consuming and involve tedious computations. Even a simple problem with few variables take a long time to solve manually and even by a performing computations. For this reason many of the techniques were not widely used until 60’s.
The advent of computers accelerated the wide use of O.R. techniques for solving complex business problem faced by managers and administrators in business and government. Computers provide the much needed computational support for many of techniques.
The automation of computational algorithm allows decision-makers to concentrate on problem’s formulation and the interpretation of the solution. Major computer manufacturer and vendor have developed software packages for the various computer systems providing computational support for problems to be solved by the application of O.R techniques.
The Role of computers in solving current as well as future problems can be explained with the help of following examples:
(1) Most of linear programming models involve 200 to 300 decision variable with 10 to 200 constraints. It is believed that most of the business problems particularly the blending problems of oil refineries will result on LP model with 4000 to 5000 variables and 3000 to 3500 constraints.
The problem of such a magnitude is virtually impossible to solve through manual computations. Such type of a problem may be solved by application of sophisticated software packages, e.g. IFP/ OPTILMUM, developed by EXECUCOM system corporation, Austin in Texas.
(2) It is difficult to solve manually PERT/CPM models for scheduling problems when hundreds of activities are involved. The software package CPM can handle hundreds of activities with several types of resources. It determines a schedule indicating the earliest start and finish times, the latest start and finish time and the critical activities in a project network.
The programme capabilities include the following:
(a) Computation of calendar dates,
(b) Handling multiple start and event,
(c) Accepting user schedule dates for some events of the project,
(d) Summarizing and controlling project costs by resource type, and
(e) Generating outputs in tabular and graphical form.
In addition to above software, many:
Step 1:
Converting constraints into equalities, we have:
Now we draw these equations on graph, we have to find two points from which they are passing. The two points are generally the points at which line interacts x and y axes
In equation (i) at x1 = 0 then x2 = 9
and at x2 = 0 then x1 = 9
so, two points are (0, 9) & (9,0)
Draw these two points on graph and join these two points that will be the graph of equation 1.
Clearly any point L lying on or below the line x1 + x2 = 9 will satisfy the inequality x1 + x2 ≤ 9 if x1 = 3, x2 = 3 then 3 + 3 = 6 < 9
Step 2:
Similarly procedure is now adopted which is true to plot the other three lines
2x1 + 5x2 = 36
and x1 = 4
and x2 = 5
as shown in the Fig. 2, 3 and 4
Step 3:
Find the feasible region or solution space and combine the Fig. (1), (2), (3) and (4) together, a common shaded area OABC obtained (see Fig. 5)
More packages area also available in the market for solving problems relating to Dynamic programming, Decision analysis, Inventory, Waiting line or queuing, simulation, etc.