Unit I-B
- 2. Syllabus Why Operations Research? Introduction Origin of operations research Definition of operations research Characteristics of operations research Role of operations research in decision-making Methods of solving operations research problem Phases in solving operations research problems Typical problems in operations research Scope of operations research Why to study operations research
- 3. Characteristics of Operation Research It is an interdisciplinary team approach The problems an OR analyst faces are heterogeneous in nature. Number of variables and constraints are beyond analytical ability of one person. Number of peoples from various disciplines are required to understand the problem. The apply their specialized knowledge and experience to get understanding and solution to the problem on hand. It helps in increasing the creative ability of the decision makers OR provides the managers mathematical tools, techniques and models. To analyze the problem on hand and to evaluate the result of all alternatives, optimal choice and helping in making faster and better decisions A manager without knowledge takes decisions by guessing or trail and error method. It can give troublesome result. Managers uses OR techniques will have a better creative ability.
- 4. It is a system approach Any organization, business or government or defense organization, can be considered as a system having various sub-systems. The decision made by any sub-system will have its effect on other sub-systems. Example: Decision taken by department A It will have its effect on department B When dealing with OR problems, system should be treated as a whole so inter-relationship between sub-systems. The effect of people on the entire system are kept in mind
- 5. Additional Characteristics of OR OR approaches problem solving and decision making from the total system perspective. OR not only necessarily uses interdisciplinary teams, but it also interdisciplinary; It draws on techniques from sciences like biology, physics, etc., It applies the appropriate techniques from each field to the system being studied. OR doesn’t experiment with the system itself but constructs a model of the system for conducting experiments. Model building and mathematical manipulation provide the methodology. It perhaps been the key contribution to OR. The primary focus is on decision-making Computers are used extensively.
- 7. Role of OR in Decision - Making It used intensively in business, industry and government. Many new analytical methods have evolved, such as Mathematical programming Simulation Game theory Queuing theory Networks Decision analysis Multi-criteria analysis They have powerful application to practical problems with the appropriate logical structure. An easy approach to solve such problems is to model them and try to find a possible solution to it.
- 15. Mathematical model in decision-making Make objectives explicit Identify decisions that influence objectives Clarify trade-offs among decisions and objectives Require identifications and definition of quantifiable variables Explore the interaction between variables Help to identify critical data elements and their role as model inputs. Assist in recognizing and clarifying constraints on decisions and operations Facilitate communication
- 17. Methods of solving OR problems Three methods Analytical Iterative Monte-Carlo
- 18. Analytical Methods May use mathematical techniques such as differential calculus, probability theory, etc. To find the solution of a given operations research model. Analytical method -> Method of solving -> and solution -> Analytical solution Example: Problems of inventory models. This method evaluates alternatives policies efficiently.
- 20. Iterative Method It is a numerical method. We have a large number of variables and can’t use analytical methods successfully and use iterative process. 1st ->Set of trial solution + Go on changing solution = under given set of solution + no more modification. Characteristics: The method is trial and error method used is laborious, tedious, time-consuming and costly. The solution we get may not be an accurate. It is an approximate one. We find that alter certain number of iterations, the solution can’t be improved. We have to accept it as the optimal solution.
- 22. Monte-Carlo Method It is based on the random sampling of the values of the variables from a distribution of the random variable. It uses sampling technique. A table of random numbers must be generated to solve the problems. It is simulation process
- 24. Phases in solving OR problems Formulate the problem Identify the variables and constraints Establish relationship between the variables Add constraints by constructing the model Identify the possible alternative solutions Give an optimally test to basic feasible solutions Select the optimal solution Install, test and establish the solution Establish controls, implement and maintain solution
- 25. Typical problems in OR Aircraft scheduling Architectural layout planning Computer systems design Congressional district borders Drug design optimization Emergency vehicle location Fuel blending Hospital staff scheduling Inventory management Investment management Medical diagnosis and prognosis Optimal energy distribution
- 26. Scheduling in manufacturing systems Scheduling courses in schools Telecommunication systems Vehicle routing
- 30. Scope of OR The limit of application to solve the varieties of the problems. It provides a basis for the managerial decision-making / solve the problems of systems under their control. The system may be business, industry, government or defense. The problems may certain to an individual, a group of individuals, business, etc.,
- 32. In defense operations OR originated during World War II. To war-related problems, applied team approach, and came out with various approaches to solve the problem in hand. In any war field, two or more parties are involved. Each having different resources like manpower, arms and ammunition, different strategies for implementation. Every opponent has to guess about the resources the enemy can have and courses of action to attack enemy.
- 34. In Industry World War II period for industrial world was a period of depression. The industry indulged in solving various problems. Industrialist tried contemporary successful models for solving their problems. They learnt techniques of OR can be applied to solve industrial problems. After successful results, various models have been developed to solve industrial problems. Today managers have numerous techniques to solve different types of industrial problems. Managers hand various models and computer to work out the solutions quickly.
- 36. In hospitals Many times, long queues of patients in hospitals. Only few of them get treatments on time. The rest of them have to return without treatment. The additional reasons are unavailability of desired medicines and blood, shortages of ambulances and beds, etc., These problems are conveniently solved by OR
- 38. In planning for economic growth In India, we have five-year planning for a steady economic growth. Every state government prepares plans for the balanced growth of state. Various people from various departments coordinate and plan for society economic growth. All these activities departments can use OR techniques. Questions Like: How many engineers, doctors, software tester, etc., are required in future What should be their quality to face the problem, etc., It can be easily solved.
- 42. In agriculture The population of india is exploding day by day. The demand for food products. It is also a fact that the land available for agriculture is limited. So, newer methods are required for increasing agriculture yield. Selection of land area for agriculture for sowing seeds of food grains must be done. It could result into dual advantage: One is Farmer Other is Users The farmers shouldn’t experience losses. The people should get their grains on right time and at right cost.
- 45. Why to study OR? OR wide variety of career opportunities and work styles it embraces. It specialists may be theoreticians or practitioners. They may work in academic, industry, etc., May participate in just one phase of an OR study such as modelling, analysis or implementation or participate in all portions of project. OR professionals remain generalists while others specialize in particular tools. They move from technical positions to managerial functions. OR is concerned with optimal decision making, modelling, deterministic and probabilistic systems originate from real life. Applications: Engineering, Economics, Government, Business, Natural and Social Sciences.
- 46. Structuring the real-life situation into a mathematical model, abstracting the essential elements so that a solution relevant to the decision maker’s objectives can be sough. It involves looking at the problem in the context of the entire system. Exploring the structure of such solutions. Developing systematic procedures for obtaining them. Developing a solution, including the mathematical theory. An optimal value of the system measure of possibly comparing alternative courses of action by evaluating their measure of desirability.
- 47. It involves the construction of mathematical model. The model is a collection of logical and mathematical relationships that represents the aspects of situation under study. Model describes important relationships between variables. An objective function with which alternative solution are evaluated. Constraints that restrict solutions to feasible values.
- 48. OR is provide a scientific basis to the decision-makers for solving the problems involving the interaction of various components of organization by employing a team of scientists from various disciplines. All working together for finding a solution which is in the best interest of the organization as a whole. The best solution obtained is known as optimal decision