OPERATIONS RESEARCH Basic Overview 22 01 2022 1

OPERATIONS RESEARCH Basic Overview 22 -01 -2022 1

After reading the present module, you will be able to: • • • General Objectives: Understand the concept of Operations Research Know Phases and Process of Operations Research • Specific Objectives: • • • Name the basic terms related with O. R Define basic terms related with OR. Define Operation Research Describe the phases of O. R. Draw the flow chart of O. R. approach. List out the various techniques of O. R. Give application fields of various techniques. List out the components of mathematical model. State advantages and limitations of O. R. Identify the various application fields of O. R. 22 -01 -2022 2

Module -Table of Contents • • Introduction Origin Phases and Process of OR Techniques of OR Advantages and Disadvantages Of OR Applications of OR Practice Task References 22 -01 -2022 3

Introduction Today, almost every large organization or corporation in developed nations as well as to some extent in developing countries has executive applying operations research, and in government the use of operations research has spread from military to widely varied departments at all levels. Availability of faster and flexible computing facilities and the number of qualified OR professionals has enhanced the acceptance and popularity of the discipline. The growth of OR has not been limited to the USA and the UK, now it has reached to many countries including India was one of the first few countries who started using OR. In 1949, the first OR unit was established in the Regional Research Laboratory at Hyderabad. Today, OR is a popular subject in management, mechanical engineering and the mathematics. So for engineers, the knowledge of OR is very essential not just for placement but also for career growth. This lecture gives insight into the approaches and tools of OR and identify the application areas in which OR has used successfully. 22 -01 -2022 4

ORIGIN • The ambiguous term Operations Research (OR) was coined during world war II, when the British Military Management called upon a group of scientists together to apply a scientific approach to the study of military operations to win the battle. • Operations Research originated in Great Britain during World War II to bring mathematical or quantitative approaches to bear on military operations. • The main objective was to allocate the scarce resources in an effective manner to the various military operations and to the activities within each operation. • The effectiveness of operations research in military spread in it to other government department and industry. • Due to the availability of faster and flexible computing facilities and the no. of qualified O. R. professionals, it is now widely used in military, business, industry, transportation, public health etc. • Since its birth in the 1940's, OR has been widely recognized as an important approach to decision-making in the management of all aspects of an organization. 22 -01 -2022 5

INTRODUCTION • It is concerned with co-ordinating and controlling the operations or activities within the organization. • O. R. can be regarded as the mathematical and quantitative techniques to substantiate the decisions being taken. • O. R. takes tool from subjects like statistics, mathematics, engineering, economics, psychology etc. and uses them to know the consequences of possible alternative actions. • Operations research (OR) is a discipline explicitly devoted to aiding decision makers. 22 -01 -2022 6

OPERATIONS The activities carried out in an organization related to attaining its goals and objectives. 22 -01 -2022 7

RESEARCH The process of observation and testing characterized by the scientific method. The steps of the process include observing the situation and formulating a problem statement, constructing a mathematical model, hypothesizing that the model represents the important aspects of the situation, and validating the model through experimentation. 22 -01 -2022 8

ORGANIZATION The society in which the problem arises or for which the solution is important. The organization may be a corporation, a branch of government, a department within a firm, a group of employees, or perhaps even a household or individual. 22 -01 -2022 9

DECISION MAKER An individual or group in the organization capable of proposing and implementing necessary actions. 22 -01 -2022 10

MAKING DECISIONS OR TAKING ACTIONS IS CENTRAL TO ALL OPERATION RESEARCH APPLICATIONS 22 -01 -2022 11

DEFINITIONS • OR is a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control. – Morse & Kimball • Operations research is a scientific approach to problem solving for executive management. – H. M. Wagner • Operations research is an aid for the executive in making this decisions by providing him with the needed quantitative information based on the scientific method of analysis. – C. Kittel 22 -01 -2022 12

Nature of O. R. Characteristics • • Inter-disciplinary team approach Systems approach Helpful in improving the quality of solution Scientific method Goal oriented optimum solution Use of models Require willing executives Reduces complexity 22 -01 -2022 13

PHASES OF OPERATIONS RESEARCH 22 -01 -2022 14

1. Recognize the Problem 22 -01 -2022 15

1. Recognize the Problem • Decision making begins with a situation in which a problem is recognized. • The problem may be actual or abstract, it may involve current operations or proposed expansions or contractions due to expected market shifts, it may become apparent through consumer complaints or through employee suggestions, it may be a conscious effort to improve efficiency or a response to an unexpected crisis. • It is impossible to circumscribe the breadth of circumstances that might be appropriate for this discussion, for indeed problem situations that are amenable to objective analysis arise in every area of human activity. 22 -01 -2022 16

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2. Formulate the Problem • At the formulation stage, statements of objectives, constraints on solutions, appropriate assumptions, descriptions of processes, data requirements, alternatives for action and metrics for measuring progress are introduced. • Because of the ambiguity of the perceived situation, the process of formulating the problem is extremely important. The analyst is usually not the decision maker and may not be part of the organization, so care must be taken to get agreement on the exact character of the problem to be solved from those who perceive it. There is little value to either a poor solution to a correctly formulated problem or a good solution to one that has been incorrectly formulated. 22 -01 -2022 18

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3. Construct a Model • • • A mathematical model is a collection of functional relationships by which allowable actions are delimited and evaluated. Although the analyst would hope to study the broad implications of the problem using a systems approach, a model cannot include every aspect of a situation. A model is always an abstraction that is, by necessity, simpler than the reality. Elements that are irrelevant or unimportant to the problem are to be ignored, hopefully leaving sufficient detail so that the solution obtained with the model has value with regard to the original problem. The statements of the abstractions introduced in the construction of the model are called the assumptions. It is important to observe that assumptions are not necessarily statements of belief, but are descriptions of the abstractions used to arrive at a model. The appropriateness of the assumptions can be determined only by subsequent testing of the model’s validity. Models must be both tractable -- capable of being solved, and valid -representative of the true situation. These dual goals are often contradictory and are not always attainable. We have intentionally represented the model with well-defined boundaries to indicate its relative simplicity. 22 -01 -2022 20

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4. Find a Solution(1) • The next step in the process is to solve the model to obtain a solution to the problem. It is generally true that the most powerful solution methods can be applied to the simplest, or most abstract, model. • Some methods can prescribe optimal solutions while other only evaluate candidates, thus requiring a trial and error approach to finding an acceptable course of action. • It may be necessary to develop new techniques specifically tailored to the problem at hand. A model that is impossible to solve may have been formulated incorrectly or burdened with too much detail. Such a case signals the return to the previous step for simplification or perhaps the postponement of the study if no acceptable, tractable model can be found. 22 -01 -2022 22

4. Find a Solution(2) • Of course, the solution provided by the computer is only a proposal. An analysis does not promise a solution but only guidance to the decision maker. • Choosing a solution to implement is the responsibility of the decision maker and not the analyst. The decision maker may modify the solution to incorporate practical or intangible considerations not reflected in the model. 22 -01 -2022 23

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5. Establish the Procedure(1) • Once a solution is accepted a procedure must be designed to retain control of the implementation effort. • Problems are usually ongoing rather than unique. Solutions are implemented as procedures to be used repeatedly in an almost automatic fashion under perhaps changing conditions. • Control may be achieved with a set of operating rules, a job description, laws or regulations promulgated by a government body, or computer programs that accept current data and prescribe actions. 22 -01 -2022 25

5. Establish the Procedure(2) • Once a procedure is established (and implemented), the analyst and perhaps the decision maker are ready to tackle new problems, leaving the procedure to handle the required tasks. • But what if the situation changes? • An unfortunate result of many analyses is a remnant procedure designed to solve a problem that no longer exists or which places restrictions on an organization that are limiting and no longer appropriate. • Therefore, it is important to establish controls that recognize a changing situation and signal the need to modify or update the solution. 22 -01 -2022 26

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6. Implement the Solution • A solution to a problem usually implies changes for some individuals in the organization. Because resistance to change is common, the implementation of solutions is perhaps the most difficult part of a problem solving exercise. • Some say it is the most important part. Although not strictly the responsibility of the analyst, the solution process itself can be designed to smooth the way for implementation. • The persons who are likely to be affected by the changes brought about by a solution should take part, or at least be consulted, during the various stages involving problem formulation, solution testing, and the establishment of the procedure. 22 -01 -2022 28

The OR Process • Combining the steps we obtain the complete OR process. • In practice, the process may not be well defined and the steps may not be executed in a strict order. Rathere are many loops in the process, with experimentation and observation at each step suggesting modifications to decisions made earlier. • The process rarely terminates with all the loose ends tied up. Work continues after a solution is proposed and implemented. Parameters and conditions change over time requiring a constant review of the solution and a continuing repetition of portions of the process. 22 -01 -2022 29

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O. R. APPROACH 22 -01 -2022 31

Practice Task 1. Write the name of the phases of O. R. Check your answer. 22 -01 -2022 32

Ans. Judgment Phase Research Phase Action Phase Now Answer the Next Question. 22 -01 -2022 33

Practice Task 2. Decision making begins with a situation in which a problem is recognized. (True/False) 22 -01 -2022 34

Yes, it is true. Problem is firstly identified then other phases follows. Now Answer the Next Question. 22 -01 -2022 35

No, you are wrong. If problem is not recognized at first, there will be ambiguity in the process of finding optimum solution. Now Answer the Next Question. 22 -01 -2022 36

Practice Task 3. Why formulation of problem is necessary to solve O. R. problem? Check your answer. 22 -01 -2022 37

Ans. 3 Because of the ambiguity of the perceived situation, the process of formulating the problem is extremely important. Now Answer the Next Question. 22 -01 -2022 38

Practice Task Q 4. Is initial solution of the problem is always optimum? (True/False) 22 -01 -2022 39

Yes, you are right. Always all the solutions come are not optimum, it is only guide us to tell in which direction the solution can be optimum. Now Answer the Next Question. 22 -01 -2022 40

No, you are wrong. The initial solution may or may not be optimum. There can other alternative or better solutions available. Now Answer the Next Question. 22 -01 -2022 41

Practice Task Q 5. Resistance to change is common, when the solution is implemented in the organisation. (Yes/No) 22 -01 -2022 42

Yes, you are right. During the time of new solution is implemented, the personnel of the organization resist to change the situations very often. You are excellent! Now you learn the next input. 22 -01 -2022 43

No, you are wrong. Human resource in the organization creates hurdles in changing the existing situations even in exist conditions are not conducive. You are excellent! Now you learn the next input. 22 -01 -2022 44

TECHNIQUES OF OR(1) • Linear programming- It has been used to solve problems involving assignment of jobs to machines, blending, product mix, advertising media selection, least cost diet, distribution, transportation and many others. • Dynamic programming- It has been applied to capital budgeting, selection of advertising media, cargo loading and optimal routing problems. • Waiting line or queuing theory- It has been useful to solve problems of traffic congestion, repair and maintenance of broken-down machines, number of service facilities, scheduling and control of air-traffic, hospital operations, counter in banks and railway booking agencies. • Inventory control / planning- These models have been used to determine economic order quantities, safety stocks, reorder levels, 22 -01 -2022 minimum and maximum stock level. 45

TECHNIQUES OF OR(2) • Decision theory- It has been helpful in controlling hurricuanes, water pollution, medicine, space exploration, research and development projects. • Network analysis (PERT& CPM)- These techniques have been used in planning, scheduling and controlling construction of dams, brides, roads and highways and development & production of aircrafts, ships, computers etc. • Simulation- It has been helpful in a wide variety of probabilistic marketing situations. • Theory of replacement- It has been extensively employed to determine the optimum replacement interval for three types of replacement problems: i) Items that deteriorate with time. ii) Items that do not deteriorate with time but fail suddenly. iii) Staff replacement and recruitment. 22 -01 -2022 46

What is a Mathematical Model? • The majority of practical decision problems are described in very vague terms. Therefore, a mostimportant step in a scientific or quantitative analysis of a problem is to formulate a model that adequately captures the essence of a problem. The result of such a formulation, or an abstraction, is called a mathematical optimization model. • Generally speaking, a mathematical optimization model has the following typical components: • a set of decision variables • an objective function, expressed in terms of the decision variables, that is to be minimized or maximized • a set of constraints that limit the possible values of 22 -01 -2022 variables 47 the decision

ADVANTAGES • • • Provides a tool for scientific analysis. Provides solution for various business problems. Enables proper deployment of resources. Helps in minimizing waiting and servicing costs. Enables the management to decide when to buy and how much to buy? Assists in choosing an optimum strategy. Renders great help in optimum resource allocation. Facilitates the process of decision making. Management can know the reactions of the integrated business systems. Helps a lot in the preparation of future managers. 22 -01 -2022 48

LIMITATIONS • The inherent limitations concerning mathematical expressions • High costs are involved in the use of O. R. techniques • O. R. does not take into consideration the intangible factors • O. R. is only a tool of analysis and not the complete decision-making process • Other limitations • Bias • Inadequate objective functions • Internal resistance • Competence • Reliability of the prepared solution 22 -01 -2022 49

Application Fields • • • Industry Defense Planning Agriculture Public utilities 22 -01 -2022 50

Practice Task Ques. 1 Assignment of jobs to machines problems can be solved by linear programming. True 22 -01 -2022 51

Yes, you are right. Assignment Problems is solved with the help of linear programming techniques. You are excellent! Now you are at the end. 22 -01 -2022 52

No, you are wrong. Assigning the machines problems can best be solved by linear programming techniques. You are excellent! Now you are at the end. 22 -01 -2022 53

References • Operations Research : An Overview Lecture by Mr. P. Ghosal, Department of Information Technology, Bengal Engineering & Science University, Shibpur, February 14, 2007. • Operations Research Simplified, chapter-1 from www. universalteacher. com 22 -01 -2022 54

THANKS 22 -01 -2022 55