Operations ResearchLecture Notes ByProf A K SaxenaProfessor and HeadDept of CSITG G Vishwavidyalaya, Bilaspur-IndiaOperations ResearchSome important tips before start of course material to students• Mostly we followed Book by S D Sharma, as prescribed for this syllabus• At places, we use some internet links not necessarily mentioned there at.• We acknowledge all such resources.• As the course is mostly mathematical in nature, we will be solving problems in class room. The problems will involve a lot of mathematics, calculations although simple but will be so time consuming to express on computers, we leave it up to students to ask in details any particular topic or problem in class or during contact hours.• So ready to take off !!!!History of Operations ResearchThe term Operation Research has its origin during the Second World War. The military management of England called a team of scientists to study the strategic and tactical problems which could raise in air and land defence of the country. As the resources were limited and those need to be fully but properly utilized. The team did not involve actually in military operations like fight or attending war but the team kept off the war but studying and suggesting various operations related to war.What is Operations Research?Several definitions have been given • Operations research (abbreviated as OR hereafter) is a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control: Morse and Kimbal (1944)• OR is an analytical method of problem-solving and decision-making that is useful in the management of organizations. In operations research, problems are broken down into basic components and then solved in defined steps by mathematical analysis.• Operational Research (OR) is the use of advanced analytical techniques to improve decision making. It is sometimes known as Operations Research, Management Science or Industrial Engineering. People with skills in OR hold jobs in decision support, business analytics, marketing analysis and logistics planning – as well as jobs with OR in the title.•As such a number of definitions can be found in literature, you can express the term OR with the spirit mentioned in the literature.Meaning of Operations Research?As stated early, the OR does not mean to get involved in the operations but suggestion for better execution of operations. Suggesting strategy how the operations can be improved and get better results. The genesis of OR is in finding better ways to solve a problem. Thus it is analytical not purely hard core action oriented. As we explore several options for the analysis of operations, we search and re-search the effects of operations. If one solution offers some result, try second solution and see and compare with previous and so on unless we satisfy ourselves. Therefore research term sounds to indicate that there would be enough thinking on the outcome of several results. Hence Operation Research.Meaning of Operations Research?A simple example of ORGiven different routs to reach from source A to destination B. Also on these routes there can be various ways to travel. For simplicity, we assume we have travelling modes x,y,z each having different travelling time and cost incurred on travel.I have a limited money or budget and a limited time also to reach destination B. Now all options can reach me A to B but they will not be fit for me. I want a solution which I can use so that I can afford journey both in terms of cost and time. OR can be used here.Management Applications of Operations Research?1. Finance budgeting and investment2. Purchase, procure and exploration3. Production management4. Marketing5. Personal management6. Research and developmentScopes of OR (elaborate following by your own as discussed in class) 1. Agriculture: optimum allocation of land, crops, irrigation etc2. Finance: maximize income, profit, minimize cost etc3. In industries: Allocation of resources, assignment of problems to worthy employees etc4. Personal management: To appoint best candidate, decide minimum employees to complete job etc5. Production management: Determine number of units to produce to maximize profit, etcPrinciples of Modeling in Operations Research?How should we model problems of OR, for this purpose following principles can be kept in mind (Some principles are given here)1. Try to build up a simple model in stead of building complex model2. Use only the specialized model to solve a problem rather than applying same model to fit in every problem3. Model validation before implementation: Test a model before it is actually implemented in real world 4. Model should be practical in approach and not a pure ideal one which may face problem when put in real time problems5. Use a model only for which it is best. It should not be pressed to do what it can not do better with6. OR models can support decision makers in their process but can not replace or in many cases outperform decision makers.Main Characteristics or features of Operations Research?1. Inter-disciplinary team approach: In OR, to model a problem, people or experts from various disciplines are joined. E.g Computer expert, Economists, mathematicians can join to model a economics problem2. Wholistic approach to the system: OR models have to think the whole business not for the particular unit for which it is engaged. It will see the effect of the model in entire business.3. Using OR techniques, we can only improve the solutions of the exiting problems but can not make them perfect due to many other factors affecting solutions4. Use of scientific research to apply the state of art techniquesto improve solutions5. Total output is optimized by maximizing or minimizing outputIn the present course we will consider only few well establishedstandard problems of OR like LPP, Transportation, Assignment, Replacement, CPM/PERT. Further there can be optimization models involving Genetic, Swarm intelligence, etc beyond the scope of the course hereExpression of problems in Operations Research?A typical example of OR problemMost of the problems in OR are of the following form• Given an objective function also
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