Management Science

http://v3solutions.in/ Management Science

http://v3solutions.in/ Introduction: The roots of OR extend to early 1800’s. it was in 1917. When A K Erlang, a Denish mathematician, published his work on the problem of congestion of telephone traffic. The difficulty was that during busy periods, telephone operators were unable to handle the calls the moment they were made, resulting in delayed calls. A few years after his appearance, his work was accepted by British post office as the basis of calculating circuit facilities. During the 1930’s, H C Levinson applied scientific analysis to the problems of merchandising. His work included scientific study of customers’ buying habits, response to the advertising and relation of environment to the type of article sold. Operations research (Management Science) really came to the force and became established as a subject during world war II.

http://v3solutions.in/ At that time, Britain was having very limited military resources, therefore there was an urgent need to allocate resources to the various military operations, and to the activities with in each operation in an effective manner. Therefore, the British military executives and managers called upon a team of scientists to apply scientific approach to study the strategic and tactical problems related to air and land defense of the country.

http://v3solutions.in/ Among the investigation carried out by them were the determination of (i) the optimum convoy size to minimize losses from submarine attacks, (ii) the optimum way to deploy radar units in order to maximize potential coverage against possible enemy attacks, and (iii) the investigation of new flight patterns and correct color of the aircrafts to minimize the chance of detection by the submarines. Because the team was dealing with the research on military operations, the work of this team of scientists was named as “Operations Research” in Britain. Their efforts were instrumental in winning the “Air Battle of Britain”, “Battle of North Atlantic”, etc. Post War Development: The success of this team of Britain encouraged US, Canada and France to start with such teams. The work of this team is was given various names in US: Operational Analysis, Operations Evaluation, Operations Research, System Analysis etc.

http://v3solutions.in/ WORLD WAR II, Limited Resources & Ultimate Crisis

http://v3solutions.in/ WORLD WAR II, Women Pushed Into War – Lack of Resources

http://v3solutions.in/ LIMITED RESOURCES

http://v3solutions.in/

http://v3solutions.in/ The apparent success of OR in military, attracted the attention of industrial management in the new field. In this way, OR begin to creep into industry, business and government organizations. After the war, many of the scientists were motivated to pursue research relevant to the field. The first technique in the field, called the Simplex Method for solving linear programming problem, was developed by American mathematician. George Dantzing in 1947.

http://v3solutions.in/ The Nature & Definition of OR: What is Operations Research? A number of definitions of OR has been formulated to answer this question, but none of them is complete. Few Definitions of OR: • OR is an art of winning wars without fighting them – AUTHER CLARKE. • OR is an art of giving bad answers to the problems where otherwise the worse answers are given – T. L. Saaty. • 3. OR is a management activity pursued in two complementary ways – JAGJIT SINGH.

http://v3solutions.in/ Objective of OR: The objective of OR is to provide a scientific basis to the decision makers for solving the problems involving the operations of the system to give a solution which is in the best interest of the organization. The solution is called the Optimum Solution to the problem. Phases of OR: • The various phases of Operations Research are as follows: • Formulation of the problem. • Construction of the mathematical model to represent the system under study. • Deriving the solution from the model. • Testing the model and the solution derived from it. • Implementing and maintaining the solution.

http://v3solutions.in/ Areas of Applications (Scope) of OR: • OR has got a wide scope. In general we can say that whenever there is a problem, there is OR for help. In addition to the military, operations research is widely used in many organizations including business and industry. Now we shall discuss the scope of OR in various important fields. • In Defense • In Industry • a. Production Department • b. Marketing Department • c. Financial Department • In L.I.C. • In Agriculture • In Planning

http://v3solutions.in/ Scientific Methods in OR: • The scientific methods in OR study generally involve the following phases. • The Judgment Phase • A. The determination of the operation. • B. The establishment of the objectives & the values related to the operation. • C. The determination of suitable measures of effectiveness and • D. The formulation of the problem relative to the objectives.

http://v3solutions.in/ • The Research Phase • A. Observations and data collection for a better understanding of the problem. • B. Formulation of hypothesis and models. • C. Observations and experiment to test the hypothesis on the basis of other available data. • D. Analysis of the available information. • E. Verification of the hypothesis using pre-established measures of effectiveness. F. Prediction of various results from the hypothesis. G. Generalization of the result and consideration of alternative methods.

http://v3solutions.in/ 3. The Action Phase The action phase of OR consist of making recommendation for decision process by any one in a position to make a decision influencing the operation in which the problem occurred.

http://v3solutions.in/ Characteristics of OR: • OR is the inter-disciplinary team approach to find the optimum solution. • OR emphasis on the overall approach of the system. • OR tries to optimize the total output by maximizing the profit and minimizing the cost. • OR uses scientific methods to arrive an optimum solution.

http://v3solutions.in/ Modeling in OR: Models play a very important role in OR. They are representations of reality. Models provide distilled and economic descriptions and explanations of the operations of the system that they represent. By experimenting on them, we can determine how the changes in the relevant system will effect its performance. Models enable us to experiment more effectively than on the system itself which is either impossible or too costly. “A Model in OR may be defined as an idealized representation of a real life system”

http://v3solutions.in/ • Advantage of A Model: • Models may have many advantages over a verbal description of a problem. Some of them are as follows: • It describes a problem much more concisely. • It provides some logical and systematic approach to the problem. • It indicates the limitation and scope of the problem. • It tends to make the overall structure of the problem more comprehensible. • It facilitates dealing with the problem in its entirely. • It enables the use of high – powered mathematical techniques to analyze the problem. • It helps in finding avenues for new research and improvements in a system.

http://v3solutions.in/ • Disadvantage of A Model: • Models are only an attempt in understanding an operation and should never be considered an absolute in sense. • The validity of any model with regard to the corresponding operation can only be verified by carrying in experiment and relevant data characteristics. • Characteristics of A Good Model: • It should be capable of adjusting with new formulations without having any significant change. • It should contain very few variables. • A model should not take much time in its construction.

http://v3solutions.in/ Types of Models: • Iconic Models. • Analogue Models • Symbolic Models

http://v3solutions.in/ • ICONIC MODELS: • Iconic models represents the system as it is but in different size. Thus iconic models are obtained by enlarging or reducing the size of the system. In other words they are images. • For Example: Photographs, Maps, Drawing, etc. • Advantages: • These are specific and concrete. • They are easy to construct. • These can be studied more easily than the system itself.

http://v3solutions.in/ • Disadvantages: • These are difficult to manipulate for experimental purpose. • They can not be used to study the changes in the operation of a system. • It is not easy to make any modification or improvement in these models. • Adjustments with changing situations can not be done in these models.

http://v3solutions.in/ Analogue Models: In analogue models one set of properties is used to represent another set of properties. After the problem is solved, the solution is re-interpreted in terms of the original system. For example: Graphs are analogues as distance is used to represent a wide variety of variables such as time, percentage, age, weight etc. Advantage: They are easy to manipulate then iconic models. Disadvantage: They are less specific and less concrete.

http://v3solutions.in/ • Mathematical (Symbolic) Models: • In symbolic models letters, numbers and other types of mathematical symbols are used to represent variables and relationships between them. Thus symbolic models are some kind of mathematical equations or inequalities reflecting the structure of the system they represent. Inventory models, queuing models etc., are the examples of symbolic models. • Advantage: • They are most abstract and most general. • They are usually easy to manipulate experimentally. • They usually yield more accurate results, under manipulation. • Thus, in OR, symbolic models are used whenever possible.

http://v3solutions.in/ General Methods of Solution for OR Models: • Solution of a model consist of finding the values of the controlled variables that optimize the measure of performance, or of estimating them approximately. OR models are generally solved by the following three methods: • Analytic Methods: • In these methods all the tools of classical mathematics, such as differential calculus and finite differences are available for the solution of the model. Various inventory models are solved by the use of these Analytical Models.

http://v3solutions.in/ 2. Numerical Methods: Numerical methods concerns with the iterative or trail and error methods. Whenever the classical methods fail, we use iterative procedure. The classical methods may fail because of the complexity of the constraints or of the number of variables.

http://v3solutions.in/ • In this we start with a trial solution and a set of rules for improving it. The trial solution is improved by the given rules and is then replaced by this improved solution. This process of improvement is repeated until either no further improvement is possible or when the cost of further calculation can not be justified. • Iterative Process is divided into three categories: • Here we know that each iteration will improve the solution and that after a finite number of repetitions no further improvement will be possible. • Although the successive iterations improve the solution, but here we are only guaranteed the solution as a limit of a infinite process. • Here we include trial and error methods. We only know the successive trials tend to improve the result, without being sure of monotonic improvement.

http://v3solutions.in/ • 3. Monte Carlo Technique Simulation: • The basis of Monte Carlo technique is random sampling of a variable’s possible values. For this technique some random numbers are required which may be converted into random variables whose behaviour is known from the past experience. Darker and Kac define Monte Carlo methods a combination of probability methods and sampling techniques providing solutions to complicated partial or integral differential equations. In short Monte Carlo Technique is concerned with experiments on random numbers and it provide solutions to complicated OR problems. Monte Carlo Techniques are useful in the following situations: • Where one is dealing with a problem which have not yet arisen i.e., where it is not possible to gain any information from past experience. • Where the mathematical and statistical problems are too complicated and some alternative methods are needed. • To estimate the parameters of a model.

http://v3solutions.in/ • The main step of Monte Carlo Techniques are as follows: • To get the general idea of the system, a flow diagram is drawn. • Then correct sample observations are taken to select some suitable model for the system. In this step some probability distribution for the variables of our interest is determined.

http://v3solutions.in/ • Then the probability distribution is converted to a cumulative distribution function. • Then a sequence of random numbers is selected with the help of random number tables. • Then the sequence of values of the variables of our interest is determined with the sequence of random numbers obtained in step 4. • Finally, some standard mathematical function is applied to the sequence of values obtained in step 5.

http://v3solutions.in/ • Advantages: • They are helpful in finding solutions of complicated mathematical expressions which is not possible otherwise. • By these methods difficulties of trial and experimentation are avoided. • Disadvantages: • These are costly way of getting a solution to any problem. • These methods do not provide optimal answers to the problems. The answers are good only when the size of samples are sufficiently large.

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Management Science