1-Introduction to OR.ppt

INTRODUCTION TO OPERATIONS RESEARCH What is Operations Research (OR)? Operations Research [Management Science] is the application of scientific methods, techniques, and tools to problems involving the operation of systems so as to provide those in control of the operations...

INTRODUCTION TO OPERATIONS RESEARCH What is Operations Research (OR)? Operations Research [Management Science] is the application of scientific methods, techniques, and tools to problems involving the operation of systems so as to provide those in control of the operations with optimum, or practically optimum, solutions to the problems. What is Operations Research (OR)? The Committee on Operations Research of the National Research Council in Great Britain defines Operations Research as “the application of the scientific method to the study of the operations of large, complex organizations or activities.” OR is typically used to denote the study and development of the mathematics that underlie the techniques. However, it is frequently used interchangeably with the term management science, which has emphasis on managerial decision-making. Development of Operations Research During WWII the military management in England called on a team of scientists to study the strategic and tactical problems associated with air and land defense of the country. Their objective was to determine the most effective utilization of limited military resources. The name OPERATIONS RESEARCH was apparently coined because the team was dealing with research on military operations. http://www.youtube.com/watch?v=I43fGlSh6kA&feature=related Development of Operations Research The encouraging results achieved by the British OR teams motivated US military management to start similar activities. After the war, the success of the military teams attracted the attention of industrial managers who were seeking solutions to their problems. The first widely accepted mathematical technique in the field of OR called the Simplex Method of Linear Programming, was developed in 1947 by an American mathematician George B. Dantzig. FOCUS of OR Study The primary focus of most OR studies is the need to allocate scarce/limited resources. OR is a decision-making tool and in the right hands, its use could save an organization a lot of time and resources. Benefits of Operations Research 1. Provides a systematic and logical approach to decision-making. 2. Helps communication within an organization through consultation with experts in various areas. 3. Permits a thorough analysis of a large number of alternative options. 4. Enables evaluation of situations involving uncertainty. 5. Allows decision makers to judge how much information to gather in a given problem. Benefits of Operations Research 6. Increases the effectiveness of the decision. 7. Enables quick identification of the best available solution. 8. Allows quick and inexpensive examination of a large (sometimes infinite) number of alternatives. 9. Enables experimentation with different alternatives using models, thus eliminating the cost of making errors while experimenting with reality. Limitations of Operations Research 1. Time-consuming. 2. Probable lack of acceptance by decision makers. 3. Assessments of uncertainties are difficult to obtain. 4. Evaluates the decision in terms of a sometimes oversimplified model of reality, possibly leading to erroneous recommendations. 5. Can be expensive to undertake, relative to the size of the problem. 6. Studies may be abandoned for various reasons, resulting in an unproductive expense. Phases of an OR Study Problem Formulation 2. Construction of the Mathematical Model 3. Derivation of the Solution 4. Testing of the Model and the Solution 5. Establishing Control over the Solution 6. Implementation of the Final Results Types of Models The representation of the systems or problems through models can be done at various degrees of abstraction. Models are classified, according to their degree of abstraction, into three groups: 1. Iconic or scale models-the least abstract, is a physical replica of a system, usually based on a different scale than the original. 2. Analog models-does not look like the real system but behaves like it. These are usually two- dimensional charts or diagrams; that is, they are physical models, but their shape differs from that of the system. 3. Mathematical models-a system of mathematical symbols and expressions to represent a real situation. Structure of Mathematical Models 1. Decision variables and parameters– decision variables are the unknowns to be determined from the solution of the model. The parameters represent the controlled variables of the system. 2. Structural constraints or restrictions– to account for the physical limitations of the system, the model must include constraints which limit the decision variables to their feasible values. 3. Objective function– this defines the measure of effectiveness of the system as a mathematical function of its decision variables. Single goal to maximize or minimize Optimize X0 = f (X1, …Xn) subject to gi (Xi,…, Xn) ≤ bi, i = 1, 2,... m (ith constraint, where bi is a known constant) Xj≥ 0, j = 1,2 ,… n (nonnegativity constraint) Operations Research/ Operational Research ♦ scientific approach to managerial decision- making  characterized by its use of mathematical models study is undertaken to help in solving a decision problem When do we need OR? When problems: Get Complicated; Involve trading off quantifiable factors; Require comparison of qualitative with quantitative measures; Involve uncertainties. The OR Process involves an iterative modeling of the real world. Abstraction Abstraction Real World Real World Results and Results and OR OR Recom- Recom- MODELS MODELS mendation mendation  OR: Here, There and Everywhere Operations Research has been extensively used to help decision- makers in the private sector. ♦ Manufacturing ♦ Distribution ♦ Services The public sector/ Non Profit Organizations has benefited from the applications of Operations Research. ♦ Agriculture ♦ Water Resources/Environment ♦ Transportation ♦ Health http://www.youtube.com/watch?v=3390-IYcLiQ&feature=fvsr  The OR Analyst translates real world problems into models and recommends real world solutions. Thank you 