Basic Fundamentals of Operation Research

OPERATIONS RESEARCH : 2/23/2009 1 AN OVERVIEW OPERATIONS RESEARCH

After reading the present module, learner will be able to: : 2/23/2009 2 After reading the present module, learner 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.

Module -Table of Contents : 2/23/2009 3 Module -Table of Contents Introduction Origin Practice Task Phases and Process of OR Practice Task Techniques of OR Advantages and Disadvantages Of OR Applications of OR Practice Task References

Introduction : 2/23/2009 4 Introduction Hello learners, this is first self-learning module on Basics of Operations Research. 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. 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 is first module defines Operations Research and gives a brief historical background of it. It also gives insight into the approaches and tools of OR and identify the application areas in which OR has used successfully. ALL THE BEST for this wonderful Journey.

ORIGIN : 2/23/2009 5 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.

TIME STARVED EXECUTIVES ARE MAKING BOLDER DECISIONS WITH LESS RISK AND BETTER OUTCOMES.THEIR SECRETOPERATION RESEARCH : 2/23/2009 6 TIME STARVED EXECUTIVES ARE MAKING BOLDER DECISIONS WITH LESS RISK AND BETTER OUTCOMES.THEIR SECRETOPERATION RESEARCH

INTRODUCTION : 2/23/2009 7 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.

OPERATIONS : 2/23/2009 8 OPERATIONS The activities carried out in an organization related to attaining its goals and objectives.

RESEARCH : 2/23/2009 9 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.

ORGANIZATION : 2/23/2009 10 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.

DECISION MAKER : 2/23/2009 11 DECISION MAKER An individual or group in the organization capable of proposing and implementing necessary actions.

: 2/23/2009 12 1.The process of observation and testing characterized by the scientific method. (True/False) Practice Task

Yes, you are true. Scientific methods are employed for observation and test the situations.Now Answer the Next Question. : 2/23/2009 13 Yes, you are true. Scientific methods are employed for observation and test the situations.Now Answer the Next Question.

No, you are wrong. Unscientific methods leads to confusion and donot give reliable and valid solutions. Now Answer the Next Question. : 2/23/2009 14 No, you are wrong. Unscientific methods leads to confusion and donot give reliable and valid solutions. Now Answer the Next Question.

2. Operations Research (OR) was coined during world war II, when the _ _ _ _ _ _ _ _ _ _ Management called upon a group of scientists. : 2/23/2009 15 2. Operations Research (OR) was coined during world war II, when the _ _ _ _ _ _ _ _ _ _ Management called upon a group of scientists. Practice Task

Ans. British MilitaryYou are excellent! Now you learn the next input. : 2/23/2009 16 Ans. British MilitaryYou are excellent! Now you learn the next input.

MAKING DECISIONS OR TAKING ACTIONS IS CENTRAL TO ALL OPERATION RESEARCH APPLICATIONS : 2/23/2009 17 MAKING DECISIONS OR TAKING ACTIONS IS CENTRAL TO ALL OPERATION RESEARCH APPLICATIONS

DEFINITIONS : 2/23/2009 18 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

Nature of O.R. Characteristics : 2/23/2009 19 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

PHASES OPERATIONS RESEARCH : 2/23/2009 20 PHASES OPERATIONS RESEARCH

1. Recognize the Problem : 2/23/2009 21 1. Recognize the Problem

1. Recognize the Problem : 2/23/2009 22 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.

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2. Formulate the Problem : 2/23/2009 24 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.

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3. Construct a Model : 2/23/2009 26 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.

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4. Find a Solution(1) : 2/23/2009 28 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.

4. Find a Solution(2) : 2/23/2009 29 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.

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5. Establish the Procedure(1) : 2/23/2009 31 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.

5. Establish the Procedure(2) : 2/23/2009 32 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.

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6. Implement the Solution : 2/23/2009 34 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.

The OR Process : 2/23/2009 35 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. Rather there 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.

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O.R. APPROACH : 2/23/2009 37 O.R. APPROACH

: 2/23/2009 38 1. Write the name of the phases of O.R. Check your answer. Practice Task

Ans. Judgment Phase Research Phase Action Phase Now Answer the Next Question. : 2/23/2009 39 Ans. Judgment Phase Research Phase Action Phase Now Answer the Next Question.

2. Decision making begins with a situation in which a problem is recognized. (True/False) : 2/23/2009 40 2. Decision making begins with a situation in which a problem is recognized. (True/False) Practice Task

Yes, it is true. Problem is firstly identified then other phases follows. : 2/23/2009 41 Yes, it is true. Problem is firstly identified then other phases follows. Now Answer the Next Question.

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. : 2/23/2009 42 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.

3. Why formulation of problem is necessary to solve O.R. problem?Check your answer. : 2/23/2009 43 3. Why formulation of problem is necessary to solve O.R. problem?Check your answer. Practice Task

Ans. 3 Because of the ambiguity of the perceived situation, the process of formulating the problem is extremely important. Now Answer the Next Question. : 2/23/2009 44 Ans. 3 Because of the ambiguity of the perceived situation, the process of formulating the problem is extremely important. Now Answer the Next Question.

Q 4. Is initial solution of the problem is always optimum? (True/False) : 2/23/2009 45 Q 4. Is initial solution of the problem is always optimum? (True/False) Practice Task

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. : 2/23/2009 46 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.

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. : 2/23/2009 47 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.

Q 5. Resistance to change is common, when the solution is implemented in the organisation. (Yes/No) : 2/23/2009 48 Q 5. Resistance to change is common, when the solution is implemented in the organisation. (Yes/No) Practice Task

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. : 2/23/2009 49 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.

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. : 2/23/2009 50 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.

TECHNIQUES OF OR(1) : 2/23/2009 51 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, minimum and maximum stock level.

TECHNIQUES OF OR(2) : 2/23/2009 52 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.

What is a Mathematical Model? : 2/23/2009 53 What is a Mathematical Model? The majority of practical decision problems are described in very vague terms. Therefore, a most-important 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 the decision variables

ADVANTAGES : 2/23/2009 54 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.

LIMITATIONS : 2/23/2009 55 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

Application Fields : 2/23/2009 56 Application Fields Industry Defense Planning Agriculture Public utilities

: 2/23/2009 57 Ques. 1 Assignment of jobs to machines problems can be solved by linear programming. True Practice Task

Yes, you are right. Assignment Problems is solved with the help of linear programming techniques.You are excellent! Now you are at the end. : 2/23/2009 58 Yes, you are right. Assignment Problems is solved with the help of linear programming techniques.You are excellent! Now you are at the end.

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. : 2/23/2009 59 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.

References : 2/23/2009 60 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

THANKS : 2/23/2009 61 THANKS