UNIT_1_Introduction of OR.pdf

Introduction to Operation Research Unit-1 Introduction to Operation Research 1.1. Origin of Operations Research The subject OPERATIONS RESEARCH is a branch of mathematics - speciall...

Introduction to Operation Research Unit-1 Introduction to Operation Research 1.1. Origin of Operations Research The subject OPERATIONS RESEARCH is a branch of mathematics - specially applied mathematics, used to provide a scientific base for management to take timely and effective decisions to their problems. The British/Europeans refer to "operational research", the Americans to "operations research" - but both are often shortened to just "OR" - which is the term we will use. Operations Research is an Art and Science. It had its early roots in World War II and is flourishing in business and industry with the aid of computer You will agree that human beings have the tendency of getting maximum gains with minimum effort. The complexities in every aspect of life are increasing by the day. As a result, we would like to create/use scientific methods and techniques that help us attain optimum solutions in decision making problems. Operation Research (O.R.) is concerned with the applications of such scientific methods and techniques. “Operation” implies some action applied in any area of interest. “Research” means some organised process of getting and analysing information about the problem environment. The term Operations Research came into existence and gained prominence during the Second World War when military planners were faced with logistical tasks requiring prompt and effective solutions. Hence, a group of scientists with diverse educational backgrounds including mathematics, statistics and physics became involved in applying a scientific approach to deal with strategic and tactical problems of various military operations. This initial research on military operations soon found applications in other decision-making problems in business and industry. Hence, the word ‘military’ was dropped and it was named as ‘Operations Research’. In India, Operations Research came into existence in 1949 with the opening of an Operations Research unit at the Regional Research Laboratory in Hyderabad and also in the Defense Science Laboratory. Operations Research gained momentum in the market place in the nineteen fifties and sixties. Solutions to problems involving manufacturing processes, personnel and material planning, inventory, scheduling and others were sought through O.R. Though Operations Research had its roots in statistics, it has now acquired its own identity. Operations Research is used to solve the real-world problems that involve a lot of mathematics, statistics, computer science, accounting, etc. Operations Research has been defined in different ways by different scientists from time to time, but none of those definitions has been accepted by all. The more general and comprehensive definition of Operations Research is as follows: “Operations Research is a branch of science which is concerned with the application of scientific methods and techniques to decision making problems and with establishing the optimal solutions.” LJ Polytechnic Page 01 of 12  Fluid Mechanics and Machines 1.2 History of Operation Research Operation Research is a relatively new discipline. Whereas 70 years ago it would have been possible to study mathematics, physics or engineering (for example) at university it would not have been possible to study Operation Research, indeed the term O.R. did not exist then. It was really only in the late 1930's that operational research began in a systematic fashion, and it started in the UK. As such it would be interesting to give a short history of O.R. 1936 Early in 1936 the British Air Ministry established Bawdsey Research Station, on the east coast, near Felix Stowe, Suffolk, as the center where all pre-war radar experiments for both the Air Force and the Army would be carried out. Experimental radar equipment was brought up to a high state of reliability and ranges of over 100 miles on aircraft were obtained. It was also in 1936 that Royal Air Force (RAF) Fighter Command, charged specifically with the air defense of Britain, was first created. It lacked however any effective fighter aircraft - no Hurricanes or Spitfires had come into service - and no radar data was yet fed into its very elementary warning and control system. 1937 The first of three major pre-war air-defense exercises was carried out in the summer of 1937. The experimental radar station at Bawdsey Research Station was brought into operation and the information derived from it was fed into the general air-defense warning and control system. From the early warning point of view this exercise was encouraging, but the tracking information obtained from radar, after filtering and transmission through the control and display network, was not very satisfactory. 1938 In July 1938 a second major air-defense exercise was carried out. Four additional radar stations had been installed along the coast and it was hoped that Britain now had an aircraft location and control system greatly improved both in coverage and effectiveness. Not so! The exercise revealed, rather, that a new and serious problem had arisen. This was the need to coordinate and correlate the additional, and often conflicting, information received from the additional radar stations. With the outbreak of war apparently imminent, it was obvious that something new - drastic if necessary - had to be attempted. Some new approach was needed. 1939 In the summer of 1939 Britain held what was to be its last pre-war air defense exercise. It involved some 33,000 men, 1,300 aircraft, 110 antiaircraft guns, 700 searchlights, and 100 barrage balloons. This exercise showed a great improvement in the operation of the air defense warning and control system. The contribution made by the OR team was so apparent that the Air Officer Commander-in-Chief RAF Fighter Command (Air Chief Marshal Sir Hugh Dowding) requested that, on the outbreak of war, they should be attached to his headquarters at Stanmore in north London. 1940 On May 15th 1940, with German forces advancing rapidly in France, Stanmore Research Section was asked to analyses a French request for ten additional fighter squadrons (12 aircraft a squadron - so 120 aircraft in all) when losses were running at some three squadrons every two days (i.e. 36 aircraft every 2 days). They prepared graphs for Winston Churchill (the British Prime Minister of the time), based upon a study of current daily losses and replacement rates, indicating how rapidly such a move would deplete fighter strength. No aircraft were sent and most of those currently in France were recalled. LJ Polytechnic Page 02 of 12  Introduction to Operation Research Unit-1 1941 In 1941, an Operational Research Section (ORS) was established in Coastal onwards Command which was to carry out some of the most well-known OR work in World War II. The responsibility of Coastal Command was, to a large extent, the flying of long- range sorties by single aircraft with the object of sighting and attacking surfaced U-boats (German submarines). The technology of the time meant that (unlike modern day submarines) surfacing was necessary to recharge batteries, vent the boat of fumes and recharge air tanks. Moreover, U-boats were much faster on the surface than underwater as well as being less easily detected by sonar. 1.3. Stages of Development of Operations Research The stages of development of O.R. are also known as phases and process of O.R, which has six important steps. These six steps are arranged in the following order: Step I: Observe the problem environment Step II: Analyze and define the problem Step III: Develop a model Step IV: Select appropriate data input Step V: Provide a solution and test its reasonableness Step VI: Implement the solution The process, process activities, and process output are summarized in the following Table Process Process Activities Process Output Step 1: Observe the Site visits, Conferences, Sufficient information and problem environment Observations, Research support to proceed Step 2: Analyze and define Define: Use, Objectives, Clear grasp of need for and the problem limitations nature of solution requested Step 3: Develop a Model Define interrelationships, Models that work under stated formulate equations, Use environmental constraints known O.R. Model, Search alternate Model Step 4: Select appropriate Analyze: internal-external Sufficient inputs to operate and data input data, facts Collect options, test model Use computer data banks Step 5: Provide a solution Test the model, find Solution(s) that support current and test its reasonableness limitations, update the organizational goals model Step 6: Implement the Resolve behavioural issues Improved working and solution Sell the idea, Give Management support for longer explanations, Management run operation of model involvement LJ Polytechnic Page 01 of 12  Fluid Mechanics and Machines 1.4 Scope of Operations Research O.R. has a wide scope in everyday life as it provides better solutions to various decision-making problems with great speed and competence. It finds applications in a wide range of areas including defense operations, planning, agriculture, industry (finance, marketing, personal management, production management), research and development. We now describe the applications briefly: 1.4.1 In Defense Operations Since the Second World War, Operations Research techniques have been used for defense operations with the objective of getting maximum gains with minimum effort. It has been used for coordinating various activities of Air Force, Army and Navy. Decisions regarding formulation and selection of strategies of the various available courses of action are taken by a team of scientists. 1.4.2 In Planning for Economic Development Careful planning is necessary for economic development of any country. Operations Research is used to frame future economic and social policies. 1.4.3 In Agriculture Agricultural output needs to be increased due to increasing needs for adequate quantity and quality of food for our increasing population. But there are a number of restrictions under which agricultural production is studied. Problems of agricultural production under various restrictions such as optimum allocation of land to various crops in accordance with the climatic conditions, optimum distribution of water from various resources for irrigation purposes can easily be solved by application of Operations Research techniques. 1.4.4 In Industry Now-a-days, due to complexities of operations and huge sizes of industries, important decisions regarding various sections of the organization, e.g., planning, procurement, marketing, finance, etc. have to be taken division wise. For example, the production department needs to minimize the cost of production, but maximize output; the finance department needs to optimize capital investment; the personnel department needs to appoint competent work force at minimum cost. Each department has to plan its own objectives which may be in conflict with the objectives of other departments and may not conform to the overall objectives of the organization. For example, the sales department of an organization may want to keep sufficient stocks in the inventory, whereas the finance department may want to have minimum investment. In that case, both departments would be in conflict with each other. The applications of O.R. techniques to such situations help in overcoming this difficulty by evolving an optimal strategy and serving efficiently the interest of the organization as a whole. Finance department of an organization needs to optimize capital investment, determine optimal replacement strategies, apply cash flow analysis for long range capital investments, and formulate credit policies, credit risks, and breakeven analysis. All these can be attained by applying Operations Research techniques. The marketing department of any organization has to face various problems like product selection, formulation of competitive strategies, sales forecasting, distribution strategies, selection of advertising media with respect to cost and time, finding the optimal number of salesmen, finding optimum time to launch a product. All such problems can be overcome using Operations Research methods. Personnel Management of an organization needs to find the best combination of workers in different categories with respect to costs, skills, age and nature of jobs. It also needs to forecast the work force requirement, frame recruitment policies, assign jobs to machines or workers, LJ Polytechnic Page 02 of 12  Introduction to Operation Research Unit-1 and negotiate in a bargaining situation, etc. This can be achieved very easily by the application of Operations Research techniques. 1.4.5 In Research and Development Operations Research helps in planning and control of new research and development projects. It also helps in planning the launch of new products. Operations Research helps in solving many other problems faced by public as well as private sectors such as the ones in economic and social planning, management of natural resources, energy, housing, pollution control, waiting lines and administrative problems, insurance policies, and many more. 3.5. Where is Operation Research Used? i. Product selection, competitive actions, ii. Number of salesmen, frequencies of Finance and Banking calling on iii. Advertising strategies with respect to cost and time 3.6 Application of Operations Research in Managerial Decision Making. Operation research or management science, as the name suggests, is the science of managing. As is known, management is most of the time making decision. It is thus a decision science which helps management to make better decision. Operations research and management decision-making techniques provide a range of benefits for hospitality managers, including efficient resource management, improved decision-making, real-time data analysis, and strategic planning. By choosing the right techniques, managers can LJ Polytechnic Page 01 of 12  Fluid Mechanics and Machines streamline decision-making processes and focus on growing their business. So, if you’re looking to optimize your hospitality operations, it’s time to consider implementing OR and management decision-making techniques. Allocation and Distribution Production and Facility Planning Procurement Marketing Finance Personnel Research and Development 3.7 Some Definitions of Operation Research According to the Operational Research Society of Great Britain “Operational Research is the attack of modern science on complex problems arising in the direction and management of large systems of Men, Machines, Materials and Money in Industry, Business, Government and Defense. Its distinctive approach is to develop a scientific model of the system, incorporating measurements of factors such as Change and Risk, with which to predict and compare the outcomes of alternative Decisions, Strategies or Controls. The purpose is to help management determine its policy and actions scientifically”. According to Operation Research Society of America. “Operation Research is an experimental and applied science devoted to observing, understanding and predicting the behavior of purposeful man-machine systems; and operation research workers are actively engaged in applying this knowledge to practical problems in business, government and society.” According Morse and Kimball, “Operation Research is a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control” According Miller and Starr, “Operation Research is applied decision theory, which uses any scientific, mathematical or logical means to attempt to cope with the problems that confront the executive, when he tries to achieve a thorough-going rationality in dealing with his decision problem”. According to C.W. Churchman, “Operation Research is the application of scientific methods, techniques and tools to problem involving the operation of a system so as to provide those in control of the system with optimum solution to the problem.” According to C. Kittel, “Operation Research is an aid for the executive in making his decision by providing him with the needed quantitative information based on the scientific methods of analysis.” According to H.M. Wanger, “Operation Research is a scientific approach to problem solving for executive management.” 3.8 Operations Research in India In India, operation research came into existence with the opening of an OR unit in 1949 at the Regional Research Laboratory in Hyderabad. At the same time another OR was set up at the Defense Science Laboratory to tackle the problems of stores, purchase and weapon evaluation. An OR unit under professor P.C. Mahalonobis was established in 1953 in the Indian Statistical Institute, Kolkata to apply OR methods in national planning and survey. Operation Research Society of India (ORSI) was formed in 1957 and its first conference was held in Delhi in 1959. LJ Polytechnic Page 02 of 12  Introduction to Operation Research Unit-1 For academic studies, the first M.Sc. course on OR was started by Delhi University in 1963. At the same time, Institutes of Management at Kolkata and Ahmedabad introduced OR in their MBA courses. In the industrial sector, organized industries in India are becoming conscious of the role of operation research and a good number of them have well trained OR terms. Some of the Indian organizations, using OR techniques are: Airlines, Railways, Defense Organizations, Fertilizer Corporation of India, Hindustan Steel Ltd., Tata Iron and Steel Co., TELCO, DCM, CSIR, STC, BHEL, SAIL, ONGC etc. 3.9 Advantages of Operation Research Study 1. Provide Better Systems An O.R. technique is frequently adopted to examine a specific decision-making issue, such as the best factory site or whether to construct a new warehouse. Additionally, it helps select cost-effective transportation methods, work sequencing, production planning, replacement of outdated machinery, etc. 2. Enhanced Productivity Operations research contributes to boosting an organization's production. Before making a critical choice, operations controls provide managers with valuable information. It helps a business make small decisions that build up to big ones. Daily duties like inventory management, personnel planning, business development, installation, and technological upgrades are also made easier with its aid. Making correct and effective decisions aids in increasing an organization's productivity. 3. Best Control The management of big firms understands how hard and expensive it is to supervise every regular task continuously. An O.R. method could give the executive a quantitative and analytical foundation to pinpoint the issue. Applications in this area that are implemented most commonly deal with inventory replenishment and production schedule. 4. Provides Many Alternatives Management is in charge of making critical organizational choices. Operations research offers several solutions to a single issue, assisting management in selecting the best option and putting it into practice to achieve the desired result. 5. Improved Coordination The coordination between a company's many departments and employees is improved by operations research because operations research concentrates not on a single department but the entire organization. As a result, managers in each area know what must be done to advance the organization's overall goal. 6. Better Decision Making O.R. models increase decision-making and lower the possibility of making bad decisions. The O.R. technique improves the executive's understanding of his decision-making process. 7. Reduce Chances of Failure Operations and research managers discover all potential solutions for a given problem with the aid of operations, reducing the risk of failure. Before adopting a solution, all potential hazards are examined. As a result, until an unforeseen event occurs, the probability of failure decreases. LJ Polytechnic Page 01 of 12  Fluid Mechanics and Machines 3.10 Dis-Advantages of Operation Research Study 1. Costly The main drawback of operations research is its high price. Operations research uses mathematical equations that are created using pricey technologies. In addition, simulations require the assistance of professionals. 2. Dependence on a Computerized System O.R. methods look for the best solution while considering all the variables. Due to the size of these components in contemporary society, describing them quantitatively and developing links between them calls for extensive computations that computers can only perform. 3. Unquantifiable Elements OR only gives a solution when all aspects of an issue can be quantified. Not all pertinent variables are amenable to quantification. In OR studies, factors that cannot be measured have no place. Models in OR do not consider emotional or qualitative elements, which may be quite significant. 4. Distance between Manager & Operations Researcher O.R. specialists have to be mathematicians or statisticians who may not be familiar with business issues. Similarly, a manager cannot comprehend the intricate functioning of O.R. There is a gap t between the two. 5. Implementation Any decision's implementation is a sensitive task. It must account for the intricacies of human relationships and behavior. Sometimes resistance is presented due to psychological issues that have nothing to do with the problem or its solution. 6. Reliance on Specialists Operations research is required to carry out by a team of specialists. Several factors are related to this, making operations research an undesirable choice for management. For instance, if there is a miscommunication between managers & OR specialists, the solutions won't work and can't be applied. Additionally, if inaccurate information is given to the experts, all solutions will be rendered useless and may even result in a loss rather than an advantage. 7. Not Realistic Experts in Operation Research create extremely complex models to address issues. These models might not be accurate. Therefore, they might not apply to real-world circumstances. 8. Complex Operation Research is a highly complicated concept. A typical manager would find it very challenging to comprehend. As a result, most managers avoid using OR techniques. 3.11 Difficulties in Operation Research 1. Formulation of the problem. 2. Data Collection 3. Study based on observation 4. Money and Time factor 5. Human Factor 6. Unquantifiable factors/non-quantifiable factors 7. The difference between a Manager and an Operation Researchers LJ Polytechnic Page 02 of 12  Introduction to Operation Research Unit-1 3.12 Limitations of Operations Research 1. Dependence on an Electronic Computer O.R. techniques try to find out an optimal solution taking into account all the factors. In the modern society, these factors are enormous and expressing them in quantity and establishing relationships among these require voluminous calculations that can only be handled by computers. 2. Non-Quantifiable Factors O.R. techniques provide a solution only when all the elements related to a problem can be quantified. All relevant variables do not lend themselves to quantification. Factors that cannot be quantified find no place in O.R. models. 3. Distance between Manager and Operations Researcher O.R. being specialist's job requires a mathematician or a statistician, who might not be aware of the business problems. Similarly, a manager fails to understand the complex working of O.R. Thus, there is a gap between the two. 4. Money and Time Costs When the basic data are subjected to frequent changes, incorporating them into the O.R. models is a costly affair. Moreover, a fairly good solution at present may be more desirable than a perfect O.R. solution available after sometime. 5. Implementation Implementation of decisions is a delicate task. It must take into account the complexities of human relations and behavior. 3.13 Operations Research Uses (Role) Operations research plays an important role in almost all areas of business decisions. Some problems where operational research (OR) approach can be used: 1. Finance, Budgeting and Investments o Credit policy analysis. o Cash flow analysis. o Dividend policies. o Investment portfolios. 2. Marketing o Product selection, timing, etc. o Advertising media, budget allocation. o Number of salesman required. o Selection of product mix. 3. Purchasing, Procurement and Exploration o Optimal buying and reordering. o Replacement policies 4. Production Management o Location and size of warehouses, factories, retail outlets, etc. o Distribution policy. o Loading and unloading facilities for trucks, etc. o Production scheduling. o Optimum product mix. o Project scheduling and allocation of resources. 5. Personnel Management o Selection of suitable personnel. LJ Polytechnic Page 01 of 12  Fluid Mechanics and Machines o Recruitment of employees. o Assignment of jobs. o Skills balancing. 6. Research and Development o Project selection. o Control of R&D projects. o Reliability and alternative design. 3.14 Operation Research Tools and Techniques Operations Research uses any suitable tools or techniques available. The common frequently used tools/techniques are mathematical procedures, cost analysis, electronic computation. However, operations researchers given special importance to the development and the use of techniques like linear programming, game theory, decision theory, queuing theory, inventory models and simulation. In addition to the above techniques, some other common tools are non- linear programming, integer programming, dynamic programming, sequencing theory, Markov process, network scheduling (PERT/CPM), symbolic Model, information theory, and value theory. There is many other Operations Research tools/techniques also exists. The brief explanations of some of the above techniques/tools are as follows: 1. Linear Programming: This is a constrained optimization technique, which optimize some criterion within some constraints. In Linear programming the objective function (profit, loss or return on investment) and constraints are linear. There are different methods available to solve linear programming. 2. Game Theory: This is used for making decisions under conflicting situations where there are one or more players/opponents. In this the motive of the players are dichotomized. The success of one player tends to be at the cost of other players and hence they are in conflict. 3. Decision Theory: Decision theory is concerned with making decisions under conditions of complete certainty about the future outcomes and under conditions such that we can make some probability about what will happen in future. 4. Queuing Theory: This is used in situations where the queue is formed (for example customers waiting for service, aircrafts waiting for landing, jobs waiting for processing in the computer system, etc). The objective here is minimizing the cost of waiting without increasing the cost of servicing. 5. Inventory Models: Inventory model make a decisions that minimize total inventory cost. This model successfully reduces the total cost of purchasing, carrying, and out of stock inventory. 6. Simulation: Simulation is a procedure that studies a problem by creating a model of the process involved in the problem and then through a series of organized trials and error solutions attempt to determine the best solution. Sometimes this is a difficult/time consuming procedure. Simulation is used when actual experimentation is not feasible or solution of model is not possible. 7. Non-linear Programming: This is used when the objective function and the constraints are not linear in nature. Linear relationships may be applied to approximate non-linear constraints but limited to some range, because approximation becomes poorer as the range is extended. Thus, the non- LJ Polytechnic Page 02 of 12  Introduction to Operation Research Unit-1 linear programming is used to determine the approximation in which a solution lies and then the solution is obtained using linear methods. 8. Dynamic Programming: Dynamic programming is a method of analyzing multistage decision processes. In this each elementary decision depends on those preceding decisions and as well as external factors. 9. Integer Programming: If one or more variables of the problem take integral values only then dynamic programming method is used. For example number or motor in an organization, number of passenger in an aircraft, number of generators in a power generating plant, etc. 10. Markov Process: Markov process permits to predict changes over time information about the behavior of a system is known. This is used in decision making in situations where the various states are defined. The probability from one state to another state is known and depends on the current state and is independent of how we have arrived at that particular state. 11. Network Scheduling: This technique is used extensively to plan, schedule, and monitor large projects (for example computer system installation, R & D design, construction, maintenance, etc.). The aim of this technique is minimize trouble spots (such as delays, interruption, production bottlenecks, etc.) by identifying the critical factors. The different activities and their relationships of the entire project are represented diagrammatically with the help of networks and arrows, which is used for identifying critical activities and path. There are two main types of technique in network scheduling, they are: Program Evaluation and Review Technique (PERT) – is used when activities time is not known accurately/ only probabilistic estimate of time is available. Critical Path Method (CPM) – is used when activities time is know accurately. 12. Information Theory: This analytical process is transferred from the electrical communication field to O.R. field. The objective of this theory is to evaluate the effectiveness of flow of information with a given system. This is used mainly in communication networks but also has indirect influence in simulating the examination of business organizational structure with a view of enhancing flow of information. 3.15 Applications of Operations Research Today, almost all fields of business and government utilizing the benefits of Operations Research. There are voluminous of applications of Operations Research. Although it is not feasible to cover all applications of O.R. in brief. The following are the abbreviated set of typical operations research applications to show how widely these techniques are used today: Accounting: o Assigning audit teams effectively o Credit policy analysis o Cash flow planning o Developing standard costs o Establishing costs for byproducts o Planning of delinquent account strategy Construction: o Project scheduling, monitoring and control o Determination of proper work force o Deployment of work force o Allocation of resources to projects LJ Polytechnic Page 01 of 12  Fluid Mechanics and Machines Facilities Planning: o Factory location and size decision o Estimation of number of facilities required o Hospital planning o International logistic system design o Transportation loading and unloading o Warehouse location decision Finance: o Building cash management models o Allocating capital among various alternatives o Building financial planning models o Investment analysis o Portfolio analysis o Dividend policy making Manufacturing: o Inventory control o Marketing balance projection o Production scheduling o Production smoothing Marketing: o Advertising budget allocation o Product introduction timing o Selection of Product mix o Deciding most effective packaging alternative Organizational Behavior / Human Resources: o Personnel planning o Recruitment of employees o Skill balancing o Training program scheduling o Designing organizational structure more effectively Purchasing: o Optimal buying o Optimal reordering o Materials transfer Research and Development: o R & D Projects control o R & D Budget allocation o Planning of Product introduction LJ Polytechnic Page 02 of 12