{"id":3318,"date":"2020-02-12T05:49:43","date_gmt":"2020-02-12T05:49:43","guid":{"rendered":"https:\/\/commerceiets.com\/?p=3318"},"modified":"2020-02-12T05:49:43","modified_gmt":"2020-02-12T05:49:43","slug":"operations-research","status":"publish","type":"post","link":"https:\/\/commerceiets.com\/operations-research\/","title":{"rendered":"OPERATIONS RESEARCH FOR B.COM, BBA, M.COM &#038; MBA"},"content":{"rendered":"\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_72 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/commerceiets.com\/operations-research\/#OPERATIONS_RESEARCH\" title=\"OPERATIONS RESEARCH\">OPERATIONS RESEARCH<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/commerceiets.com\/operations-research\/#CHARACTERISTICS_OF_OR\" title=\"CHARACTERISTICS OF OR\">CHARACTERISTICS OF OR<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/commerceiets.com\/operations-research\/#METHODOLOGY_OF_OPERATIONS_RESEARCH\" title=\"METHODOLOGY OF OPERATIONS RESEARCH\">METHODOLOGY OF OPERATIONS RESEARCH<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/commerceiets.com\/operations-research\/#SCOPE_OF_OPERATIONS_RESEARCH\" title=\"SCOPE OF OPERATIONS\nRESEARCH\">SCOPE OF OPERATIONS\nRESEARCH<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/commerceiets.com\/operations-research\/#MATHEMATICAL_TECHNIQUES_IN_OPERATIONS_RESEARCH\" title=\"MATHEMATICAL TECHNIQUES IN OPERATIONS RESEARCH\">MATHEMATICAL TECHNIQUES IN OPERATIONS RESEARCH<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/commerceiets.com\/operations-research\/#IMPORTANCE_OF_OPERATIONS_RESEARCH\" title=\"IMPORTANCE OF OPERATIONS RESEARCH\">IMPORTANCE OF OPERATIONS RESEARCH<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/commerceiets.com\/operations-research\/#ROLE_OF_OPERATIONS_RESEARCH_IN_DECISION_MAKING\" title=\"ROLE OF OPERATIONS RESEARCH IN DECISION MAKING\">ROLE OF OPERATIONS RESEARCH IN DECISION MAKING<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/commerceiets.com\/operations-research\/#LIMITATIONS_OF_OPERATIONS_RESEARCH\" title=\"LIMITATIONS OF OPERATIONS RESEARCH\">LIMITATIONS OF OPERATIONS RESEARCH<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/commerceiets.com\/operations-research\/#CONCLUSION\" title=\"CONCLUSION\">CONCLUSION<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h1 class=\"has-text-align-center wp-block-heading\" id=\"operations-research\"><span class=\"ez-toc-section\" id=\"OPERATIONS_RESEARCH\"><\/span>OPERATIONS RESEARCH<span class=\"ez-toc-section-end\"><\/span><\/h1>\n\n\n\n<p>Operations research (OR) is an analytical method of problem-solving and decision-making that is useful in the <a href=\"https:\/\/commerceiets.com\/management\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"management (opens in a new tab)\">management<\/a> of organizations. In operations research, problems are broken down into basic components and then solved in defined steps by mathematical analysis.<\/p>\n\n\n\n<p>The concept of OR arose during World War II by military planners. After the war, the techniques used in their operations research were applied to addressing problems in business, the government and society.<\/p>\n\n\n\n<p><strong>ACCORDING TO THE OPERATIONAL RESEARCH SOCIETY OF GREAT BRITAIN <\/strong><\/p>\n\n\n\n<p>\u201cOperational Research is the attack of modern science on\ncomplex problems arising in the direction and management of large systems of\nmen, machines, materials and money in industry, business, government and\ndefense. Its distinctive approach is to develop a scientific model of the\nsystem, incorporating measurements of factors such as change and risk, with\nwhich to predict and compare the outcomes of alternative decisions, strategies\nor controls. The purpose is to help management determine its policy and actions\nscientifically.\u201d<\/p>\n\n\n\n<p><strong>&nbsp;ACCORDING TO RANDY ROBINSON <\/strong><\/p>\n\n\n\n<p>\u201cOperations Research is the application of scientific\nmethods to improve the effectiveness of operations, decisions and management.\nBy means such as analyzing data, creating mathematical models and proposing\ninnovative approaches, Operations Research professionals develop scientifically\nbased information that gives insight and guides decision making. They also\ndevelop related software, systems, services and products.\u201d<\/p>\n\n\n\n<p><strong>ACCORDING TO P.M. MORSE AND G.E. KIMBALL <\/strong><\/p>\n\n\n\n<p>\u201cO.R. is a scientific method of providing executive\ndepartments with a quantitative basis for decisions regarding the operations\nunder their control\u201d. <\/p>\n\n\n\n<p><strong>ACCORDING TO T L SATTY <\/strong><\/p>\n\n\n\n<p>\u201cO.R. is the art of giving bad answers to problems which\notherwise have worse answers\u201d. <\/p>\n\n\n\n<p><strong>ACCORDING TO MILLER AND STARR <\/strong><\/p>\n\n\n\n<p>\u201cO.R. is applied decision theory, which uses any scientific,\nmathematical or logical means to attempt to cope with the problems that\nconfront the executive, when he tries to achieve a thorough-going rationality\nin dealing with his decision problem\u201d. <\/p>\n\n\n\n<p><strong>ACCORDING TO POCOCK <\/strong><\/p>\n\n\n\n<p>\u201cO.R. is scientific methodology (analytical, mathematical,\nand quantitative) which by assessing the overall implication of various\nalternative courses of action in a management system provides an improved basis\nfor management decisions\u201d.<\/p>\n\n\n\n<p><strong>ACCORDING TO AURTHER CLARKE<\/strong><\/p>\n\n\n\n<p>\u201cOperations Research is the art of winning wars without\nactually fighting\u201d.<\/p>\n\n\n\n<p><strong>ACCORDING TO J. STEINHARDT<\/strong><\/p>\n\n\n\n<p>\u201cOperations Research is Research into Operations\u201d. <\/p>\n\n\n\n<p><strong>ACCORDING TO EL ARNOFF and M J NETZONG<\/strong><\/p>\n\n\n\n<p>\u201cOperations research is the systematic method oriented study\nof the basic structure, characteristics, functions and relationships of an\norganization decision making to provide the executive with sound, scientific\nand quantitative basis for decision making.\u201d<\/p>\n\n\n\n<p>Operations Research takes tools from different discipline\nsuch as mathematics, statistics, economics, psychology, engineering etc. and\ncombines these tools to make a new set of knowledge for decision making. Today,\nO.R. became a professional discipline which deals with the application of\nscientific methods for making decision, and especially to the allocation of\nscarce resources. The main purpose of O.R. is to provide a rational basis for decisions\nmaking in the absence of complete information, because the systems composed of\nhuman, machine, and procedures may do not have complete information.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"characteristics-of-or\"><span class=\"ez-toc-section\" id=\"CHARACTERISTICS_OF_OR\"><\/span>CHARACTERISTICS OF OR<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The features of Operations Research are as follows:<\/p>\n\n\n\n<p><strong>OPERATIONS RESEARCH\nIS AN INTERDISCIPLINARY TEAM APPROACH:<\/strong><\/p>\n\n\n\n<p>The problems an operations research analyst face is\nheterogeneous in nature, involving the number of variables and constraints,\nwhich are beyond the analytical ability of one person. Hence people from various\ndisciplines are required to understand the operations research problem, who\napplies their special knowledge acquired through experience to get a better view\nof cause and effects of the events in the problem and to get a better solution\nto the problem on hand. This type of team approach will reduce the risk of\nmaking wrong decisions.<\/p>\n\n\n\n<p><strong>OPERATIONS RESEARCH\nINCREASES THE CREATIVE ABILITY OF THE DECISION MAKER:<\/strong><\/p>\n\n\n\n<p>Operations Research provides manager mathematical tools,\ntechniques and various models to analyse the problem on hand and to evaluate\nthe outcomes of various alternatives and make an optimal choice. This will\ndefinitely helps him in making better and quick decisions. A manager, without\nthe knowledge of these techniques has to make decisions by thumb rules or by\nguess work, which may click some times and many a time put him in trouble. Hence,\na manager who uses Operations Research techniques will have a better creative ability\nthan a manager who does not use the techniques.<\/p>\n\n\n\n<p><strong>OPERATIONS RESEARCH\nIS A SYSTEMS APPROACH:<\/strong><\/p>\n\n\n\n<p>A business or a Government organization or a defense\norganization may be considered as a system having various sub-systems. The\ndecision made by any sub-system will have its effect on other sub-systems. Say\nfor example, a decision taken by marketing department will have its effect on\nproduction department. When dealing with Operations Research problems, one has\nto consider the entire system, and characteristics or sub- systems, the inter-relationship\nbetween sub-systems and then analyse the problem, search for a suitable model\nand get the solution for the problem. Hence we say Operations Research is a\nSystems Approach.<\/p>\n\n\n\n<p><strong>WHOLISTIC\nAPPROACH TO THE SYSTEM:<\/strong><\/p>\n\n\n\n<p>While evaluating any decision, the important\ninteractions and their impact on the whole organisation against the functions\noriginally involved are reviewed.<\/p>\n\n\n\n<p><strong>OBJECTIVE\nAPPROACH:<\/strong><\/p>\n\n\n\n<p>O.R. attempts to find the best or optimal\nsolution to the prob\u00adlem under consideration, taking into account the goals of\nthe organisation.<\/p>\n\n\n\n<p><strong>SCIENTIFIC APPROACH:<\/strong><\/p>\n\n\n\n<p><em>ACCORDING TO P.M. MORSE AND G.E. KIMBALL <\/em><\/p>\n\n\n\n<p>\u201cO.R. is a scientific method of providing executive\ndepartments with a quantitative basis for decisions regarding the operations\nunder their control\u201d. <\/p>\n\n\n\n<p>So OR is a proper scientific approach to solve the complex business problems. The scientific methods in Operations Research consist of three phases:<\/p>\n\n\n\n<p><strong>Judgement Phase:<\/strong> This phase consists of:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Determination of operations.<\/li><li>Establishment of objective and values related to the operation.<\/li><li>Determination of the suitable measures of effectiveness.<\/li><li>Formulation of the problems relative to objectives.<\/li><\/ul>\n\n\n\n<p><strong>Research Phase: <\/strong>This phase utilizes:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Operations and data collection for a better understanding of the\nproblem.<\/li><li>Formulation of hypothesis and model.<\/li><li>Observation and experimentation to test the hypothesis on the\nbasis of additional data.<\/li><li>Analysis of the available information and verification of the\nhypothesis using pre-established measures of effectiveness.<\/li><li>Prediction of various results from the hypothesis.<\/li><li>Generalization of the various result and consideration of\nalternative methods.<\/li><\/ul>\n\n\n\n<p><strong>Action Phase:<\/strong> It consists of making recommendations for the decision process by those who first posed the problem for consideration or by anyone in a position to make a decision, influencing the operation in which the problems occurred.<\/p>\n\n\n\n<p><strong>USE OF COMPUTER<\/strong><\/p>\n\n\n\n<p>Operations Research often requires a computer\nto solve the computer mathematical model or to perform a large number of\ncomputations that are involved. Use of a digital computer has become an\nintegral part of the operations research approach to decision making.<\/p>\n\n\n\n<p><strong>QUANTITATIVE SOLUTION<\/strong><\/p>\n\n\n\n<p><em>ACCORDING TO EL ARNOFF and M J NETZONG<\/em><\/p>\n\n\n\n<p>\u201cOperations research is the systematic method oriented study\nof the basic structure, characteristics, functions and relationships of an\norganization decision making to provide the executive with sound, scientific\nand quantitative basis for decision making.\u201d<\/p>\n\n\n\n<p>The above definition clearly states that the solutions derived by applying the OR methods and techniques are quantitative in nature as the all techniques applied are mathematical. Operations research attempts to provide a systematic and rational approach for quantitative solutions to the various managerial problems.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"methodology-of-operations-research\"><span class=\"ez-toc-section\" id=\"METHODOLOGY_OF_OPERATIONS_RESEARCH\"><\/span>METHODOLOGY OF OPERATIONS RESEARCH<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The systematic methodology\ndeveloped for O.R. study with problems involving conflicting multiple\nobjectives policies and alternatives. OR in the final analysis is a scientific\nmethodology which is applied to the study of the operations of large complex\norganizations or activities with a view to assessing the overall implications\nof various alternative courses of action thus providing an improved basis for\nmanagement decisions.<\/p>\n\n\n\n<p><strong>STEP 1.\nPROBLEM FORMULATION<\/strong><\/p>\n\n\n\n<p>This is a major phase in\nwhich the OR team should formally formulate the management problem and then\ntransform it into a research problem. For purposes of formulating the\nmanagement problem in the first instance, the OR team makes a thorough analysis\nof organizational structure and function the communication and control systems\nthe objectives and policies of&nbsp; the organization and so on<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\nIn O.R. approach problem formulation has a different meaning than what is\nunderstood in common parlance. The major components of a problem are:<\/p>\n\n\n\n<p>&#8211;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; A group or\nan individual decision maker who faces a problem.<\/p>\n\n\n\n<p>&#8211;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; The\nenvironment wherein the problem is supposed to lie. It is not unlikely that the\nroots of problem are traced to a different area. Therefore it is wise to call\nthe entire organization as the second component.<\/p>\n\n\n\n<p>&#8211;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Objectives<\/p>\n\n\n\n<p>&#8211;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\nAlternative courses of action that affect the objectives. The outcomes are not\nknown beforehand and the decision makers are in a dilemma as to which courses\nof action is to be chosen.<\/p>\n\n\n\n<p>&#8211;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\nConstraints<\/p>\n\n\n\n<p><strong>STEP 2. ANALYSIS AND DEFINING THE PROBLEM<\/strong><\/p>\n\n\n\n<p>After analyzing the\nproblem of the environment, the researcher should analyse the problem and\ndefine it in clearer terms. All the factors affecting the problems directly and\nindirectly should be taken into consideration. The in depth analysis of the\nproblem helps in its proper understanding and their contribution towards\nfinding the best solution for the problem.<\/p>\n\n\n\n<p>Example: Suppose a manager\nnotices that a reduction in sales volume is causing fall in the profit of the current\nyear. The operations researcher has been asked to analyse the problem.<\/p>\n\n\n\n<p>Now the Operations\nresearcher analyses company\u2019s products prices and promotions. He discovers that\npromotion is the main problem area. He must investigate the various variables\nresponsible for reduced sales. The culprit could be:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Amount of money spent.<\/li><li>The media used.<\/li><li>The timings of sale.<\/li><li>Or any combination of these.<\/li><\/ul>\n\n\n\n<p><strong>STEP 3.\nCOLLECTING DATA REQUIRED BY THE MODEL<\/strong><\/p>\n\n\n\n<p>\u2018Garbage In and Garbage\nOut\u2019 is the famous saying. It means if the data is inappropriate then the model\nbuilt on the basis of that data will also be inappropriate. So the data should\nbe collected very cautiously. The data may be collected from either primary or secondary\nsource. This means the researchers should conduct a fresh research to get the\ndata or should approach the historical records.<strong><\/strong><\/p>\n\n\n\n<p><strong>STEP 4.\nCONSTRUCTING A MATHEMATICAL MODEL<\/strong><\/p>\n\n\n\n<p>The next stage in the O.R\nprocess is to try to express the relevant features of the system under study in\nterms of a mathematical model. The general form a mathematical model is:<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\nE = f (x<sub>i,&nbsp;<\/sub>y<sub>i<\/sub>)<\/p>\n\n\n\n<p>Where f represents a system of mathematical relationships between\nthe measure of effectiveness of the objectives sought (E) and the variables.\nBoth controllable (x<sub>i<\/sub>) and\nuncontrollable (y<sub>i<\/sub>). <\/p>\n\n\n\n<p><strong>STEP 5.\nDERIVING SOLUTIONS FROM THE MODEL<\/strong><\/p>\n\n\n\n<p>Once the mathematical model\nis formulated the next step is to determine the value of decision variables\nthat optimize the given objective function. The various mathematical techniques\nfor arriving at such solutions comprise much of the contents of this text.<\/p>\n\n\n\n<p>In addition to the solution of the model, it is also sometimes\nessential to perform sensitivity analysis, i.e., determine the behavior of the\nsystem changes in the system parameters and specifications. This is done\nbecause the input data (parameters) may not be accurate or stable and the\nstructural assumptions of the model may not be valid. Thus sensitivity analysis\nis an essential part of this phase of the methodology and must not be\noverlooked.<\/p>\n\n\n\n<p><strong>STEP 6.\nTESTING THE MODEL<\/strong><\/p>\n\n\n\n<p>Since in once a model is\nonly a partial and simplified representation of reality, the results are to be\ntested against the real word experience in order to establish the model&#8217;s\ncredibility. Several simplifying assumptions are made while initiating the\nmodel building. These assumptions can be relaxed one by one to see the reaction\nof the model results to such relaxation.<\/p>\n\n\n\n<p>Similarly inclusion of some inappropriate variables in the model\nand exclusion of some appropriate variables from the model, just for purposes\nof abstraction and simplification may require review so that their impact on\nthe model vis-\u00e0-vis reality is analysed form a proper perspective. Model\ndistortion through simplification intentional or otherwise has to be properly\nassessed with the help of previous experience judgment actual test data and\nsimilar devices.<\/p>\n\n\n\n<p><strong>STEP 7.\nESTABLISHING CONTROLS OVER THE SOLUTION<\/strong><\/p>\n\n\n\n<p>Complex models of specific\nproblems produce decision rue ties which could be used a procedures to take\ncare of repetitive situations without having to build a model ever time. This\nnaturally calls for incorporation of controls into the model so that they are\nadaptable for a range of problem. In the dynamic business world, values of\nparameters keep changing; some parameters become outdated new parameters emerge\nunless taken care of will leave the model solution utterly useless for later\nsimilarly problems. A conscious control procedure is to be established for\ndetecting significant changes in the parameters and relationships and for\nspecifying the action to be taken or adjustments to be made in the solution\nwhen a significant change occurs.<\/p>\n\n\n\n<p><strong>STEP 8.\nIMPLEMENTING THE SOLUTION.<\/strong><\/p>\n\n\n\n<p>This is certainly the most\nimportant phase of the study, because it is only after a proposal has been\nimplemented that the benefits accrue. When an operationally feasible solution\nhas been decided upon, stage is set to put that solution into practice. This is\noften far from straight forwardness as solutions which look feasible on paper\nmay conflict drastically with the ideas and capabilities of the people involved\nin the system. Many perfectly sound (theoretically) OR recommendations do not\nreach implementation because they prove unworkable in practice.<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Finally no system is even completely static and it is always necessary to monitor the environment within which a system operates to ensure that changing conditions do not render a solution inappropriate. It is important to ensure that any solution implemented is continuously reviewed and (if necessary) updated and modified in the light of a changing environment. A changing economy, fluctuating demand and model enhancements requested by managers and decision makers are only a few examples of changes that might require the analysis to be modified.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"scope-of-operations-research\"><span class=\"ez-toc-section\" id=\"SCOPE_OF_OPERATIONS_RESEARCH\"><\/span><strong>SCOPE OF OPERATIONS\nRESEARCH<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The scope of OR is not only confined to any specific agency like\ndefense services but today it is widely used in all industrial organizations.\nIt can be used to find the best solution to any problem be it simple or\ncomplex. It is useful in every field of human activities, where optimization of\nresources is required in the best way. Thus, it attempts to resolve the\nconflicts of interest among the components of organization in a way that is\nbest for the organization as a whole. The main fields where OR is extensively\nused are given below:<\/p>\n\n\n\n<p><strong>NATIONAL PLANNING AND\nBUDGETING<\/strong><\/p>\n\n\n\n<p>OR is used for the preparation of Five Year Plans, annual\nbudgets, forecasting of income and expenditure, scheduling of major projects of\nnational importance, estimation of GNP, GDP, population, employment and\ngeneration of agriculture yields etc.<\/p>\n\n\n\n<p><strong>DEFENSE SERVICES<\/strong><\/p>\n\n\n\n<p>Basically formulation of OR started from USA army, so it has\nwide application in the areas such as:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Development of new technology<\/li><li>Optimization of cost and time <\/li><li>Tender evaluation<\/li><li>Setting and layouts of defense projects<\/li><li>Assessment of \u201cThreat analysis\u201d<\/li><li>Strategy of battle<\/li><li>Effective maintenance and replacement of\nequipment<\/li><li>Inventory control<\/li><li>Transportation and supply depots etc.<\/li><\/ul>\n\n\n\n<p><strong>R &amp; D AND\nENGINEERING<\/strong><\/p>\n\n\n\n<p>Research and development is the heart of technological\ngrowth. OR has wide scope in this field also. It can be applied in <\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Technology forecasting and evaluation<\/li><li>Technology and project management<\/li><li>Preparation of tender and negotiation<\/li><li>Value engineering<\/li><li>Work\/method study and so on.<\/li><\/ul>\n\n\n\n<p><strong>AGRICULTURE AND\nIRRIGATION<\/strong><\/p>\n\n\n\n<p>In the area of agriculture and irrigation also OR can be\nuseful for project management, construction of major dams at minimum cost,\noptimum allocation of supply and collection points for fertilizer\/seeds and\nagriculture outputs and optimum mix of fertilizers for better yield.<\/p>\n\n\n\n<p><strong>EDUCATION AND\nTRAINING<\/strong><\/p>\n\n\n\n<p>OR can be used for obtaining optimum number of schools with their\nlocations, optimum mix of students\/teacher student ratio, optimum financial outlay\nand other relevant information in training of graduates to meet out the\nnational requirements.<\/p>\n\n\n\n<p><strong>TRANSPORTATION<\/strong><\/p>\n\n\n\n<p>Transportation models of OR can be applied to real life\nproblems to forecast public transport requirements, optimum routing,\nforecasting of income and expenses, project management for railways, railway\nnetwork distribution, etc. In the same way it can be useful in the field of communication.<\/p>\n\n\n\n<p><strong>HOME MANAGEMENT AND\nBUDGETING<\/strong><\/p>\n\n\n\n<p>OR can be effectively used for control of expenses to\nmaximize savings, time management, work <\/p>\n\n\n\n<p>study methods for all related works.<\/p>\n\n\n\n<p><strong>MANUFACTURING <\/strong><\/p>\n\n\n\n<p>OR\u2019s success in contemporary business pervades manufacturing\nand service operations, logistics, distribution, transportation, and\ntelecommunication.<\/p>\n\n\n\n<p>Operations research is used to for various activities which\ninclude <\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Scheduling<\/li><li>Routing,<\/li><li>Workflow improvements<\/li><li>Elimination of bottlenecks<\/li><li>Inventory control<\/li><li>Business process re-engineering<\/li><li>Site selection<\/li><li>Facility and general operational planning.<\/li><\/ul>\n\n\n\n<p><strong>REVENUE MANAGEMENT<\/strong><\/p>\n\n\n\n<p>The application of OR in revenue management entails first to accurately forecasting the demand, and<\/p>\n\n\n\n<p>secondly to adjust the price structure\nover time to more profitably allocate fixed capacity.<\/p>\n\n\n\n<p><strong>SUPPLY CHAIN\nMANAGEMENT<\/strong><\/p>\n\n\n\n<p>In the area of Supply Chain Management, OR helps in taking decisions\nthat include the who, what, when, and where abstractions from purchasing and transporting\nraw materials and parts, through manufacturing actual products and goods, and\nfinally distributing and delivering the items to the customers. The primary\nobjective here is to reduce overall cost while processing customer orders more\nefficiently than before. The power of utilizing OR methods allows examining a rather\ncomplex and convoluted chain in a comprehensive manner, and to search among a vast\nnumber of combinations for the resource optimization and allocation strategy\nthat seem most effective, and hence beneficial to the operation.<\/p>\n\n\n\n<p><strong>RETAILING<\/strong><\/p>\n\n\n\n<p>In supermarkets, data from store loyalty card schemes is\nanalyzed by OR groups to advice on merchandising policies and profitability\nimprovement. OR methods are also used to decide when and where new store\ndevelopments should be made.<\/p>\n\n\n\n<p><strong>FINANCIAL SERVICES<\/strong><\/p>\n\n\n\n<p>In financial markets, OR practitioners address issues such\nas portfolio and risk management and planning and analysis of customer service.\nThey are widely employed in Credit Risk Management\u2014a vital area for lenders\nneeding to ensure that they find the optimum balance of risk and revenue. OR\ntechniques are also applied in cash flow analysis and capital budgeting.<\/p>\n\n\n\n<p><strong>MARKETING MANAGEMENT<\/strong><\/p>\n\n\n\n<p>OR helps marketing manager in making the apt selection of product\nmix. It helps them in making optimum sales resource allocation and assignments.<\/p>\n\n\n\n<p><strong>HUMAN RESOURCE\nMANAGEMENT<\/strong><\/p>\n\n\n\n<p>OR techniques are being applied widely in the functional area\nof Human Resource Management by helping the human resource managers in\nactivities like <\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Manpower planning<\/li><li>Resource allocation<\/li><li>Staffing and scheduling of training programs.<\/li><\/ul>\n\n\n\n<p><strong>GENERAL MANAGEMENT<\/strong><\/p>\n\n\n\n<p>OR helps in designing Decision Support System and management\nof information systems, organizational design and control, software process\nmanagement and Knowledge Management.<\/p>\n\n\n\n<p><strong>PRODUCTION SYSTEMS <\/strong><\/p>\n\n\n\n<p>The area of operations research that concentrates on real-world operational problems is known as production systems. Production systems problems may arise in settings that include, but are not limited to, manufacturing, telecommunications, health-care delivery, facility location and layout, and staffing.<\/p>\n\n\n\n<p><strong>REAL LIFE EXAMPLES OF OPERATIONS RESEARCH<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>In 2013, Dutch Delta program Commissioner used\nmixed integer programming to derive an optimal investment strategy for\nstrengthening dykes for protections against high water and keeping fresh water\nsupplies upto standard, resulting in savings of 8 billion Euros in investment\ncosts.<\/li><li>In 2012, TNT Express developed a portfolio of\nmulti- commodity and vehicle routing models for package and vehicle routing and\nscheduling, planning of pickup and delivery and supply chain optimization for\nits operations across 200 countries using 2,600 facilities, 30,000 road\nvehicles and 50 aircraft resulting in savings of 207 million euros over the\nperiod 2008-2011 and reduction in Carbon-dioxide emissions by 283 million\nkilograms.<\/li><\/ul>\n\n\n\n<ul class=\"wp-block-list\"><li>In 2010, Mexico\u2019s central security depository, INDEVAL used linear programming to develop a secure and automatic clearing and settlement engine to determine the set of transactions that can be settled to maximize the number of traded securities, thereby efficiently processing  <\/li><\/ul>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"mathematical-techniques-in-operations-research\"><span class=\"ez-toc-section\" id=\"MATHEMATICAL_TECHNIQUES_IN_OPERATIONS_RESEARCH\"><\/span><strong>MATHEMATICAL TECHNIQUES IN OPERATIONS RESEARCH<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The significant mathematical techniques of OR which has been\nsuccessfully applied to decision making are the following:<\/p>\n\n\n\n<p><strong>LINEAR PROGRAMMING&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/strong><\/p>\n\n\n\n<p>Linear Programming (LP) is a mathematical\ntechnique. It is the process of taking various linear inequalities\nrelating to some situation, and finding the &#8220;best&#8221; value obtainable\nunder those conditions. In &#8220;real life&#8221;, linear programming is part of\na very important area of mathematics called &#8220;optimization techniques\u201d. It\ntakes all kinds of factors into consideration to determine the best combination\nof a purchasing or manufacturing process, to either maximize profit, minimize\ncost or some other goal. Therefore, LP is a very important part of any\nbusiness.<\/p>\n\n\n\n<p><strong>TRANSPORTATION PROBLEM<\/strong><\/p>\n\n\n\n<p>The transportation problem is a special\ntype of linear programming problem, where the objective is to minimize\nthe cost of distributing a product from a number of sources to a number of\ndestinations. Transportation helps shape an area\u2019s economic health and quality\nof life.<\/p>\n\n\n\n<p><strong>ASSIGNMENT PROBLEM<\/strong><\/p>\n\n\n\n<p>In a few words, when the problem\ninvolves the allocation of n different facilities to n different tasks, it is\noften termed as an assignment problem. Assignment deals with the question how\nto assign n object to m other object in an injective fashion in the best possible\nway. An assignment problem is specified by its two component: <\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>The assignment which represent the underlying\ncombinatorial structure <\/li><li>The objective function to be optimized which\nmodel \u201cthe best possible way\u201d <\/li><\/ul>\n\n\n\n<p><strong>QUEUING THEORY<\/strong><\/p>\n\n\n\n<p>The queuing problem is identified\nby the presence of a group of customers who arrive randomly to receive some\nservice. Queuing theory deals with problems which involve queuing (or waiting).\nThis theory helps in calculating the expected number of people in the queue,\nexpected waiting time in the queue, expected idle time for the server, etc. <\/p>\n\n\n\n<p><strong>GAME THEORY<\/strong><\/p>\n\n\n\n<p>Game theory is the formal study of\ndecision-making where several players must make choices that potentially\naffect the interests of the other players. It is used for decision making under\nconflicting situations where there are one or more opponents (i.e., players).\nIn the game theory, we consider two or more persons with different objectives,\neach of whose actions influence the outcomes of the game. Game theory is a\nmathematical method for analyzing calculated circumstances, such as in games,\nwhere a person\u2019s success is based upon the choices of others.<\/p>\n\n\n\n<p><strong>INVENTORY CONTROL MODELS<\/strong><\/p>\n\n\n\n<p>The literal meaning of inventory is \u201cidle but usable\nresources. Thus, this model is concerned with the acquisition, storage,\nhandling of inventories so as to ensure the availability of material whenever\nneeded and minimize wastage and losses. <\/p>\n\n\n\n<p><strong>GOAL PROGRAMMING<\/strong><\/p>\n\n\n\n<p>It is a powerful tool to tackle multiple\nand incompatible goals of an enterprise. Goal programming models are\nvery similar to linear programming models but whereas linear programs have one\nobjective goal programs can have several objectives.<\/p>\n\n\n\n<p><strong>SIMULATION<\/strong><\/p>\n\n\n\n<p>It is a technique that involves setting\nup a model of real situation and then performing experiments. Simulation\nis used where it is very risky, cumbersome, or time consuming to conduct real\nexperiment to know more about a situation. <\/p>\n\n\n\n<p><strong>NONLINEAR PROGRAMMING<\/strong><\/p>\n\n\n\n<p>These methods may be used when either the\nobjective function or some of the constraints are not linear in nature.\nNon-Linearity may be introduced by factors such as discount on price of\npurchase of large quantities. <\/p>\n\n\n\n<p><strong>INTEGER PROGRAMMING<\/strong><\/p>\n\n\n\n<p>These methods may be used when one or more of the variables\ncan take only integral values. The Integer Programming problem (IP) is that of\ndeciding whether there exists an integer solution to a given set of m rational\ninequalities on n variables. E.g. the number of trucks in a fleet, the number\nof generators in a power house, etc. <\/p>\n\n\n\n<p><strong>DYNAMIC PROGRAMMING<\/strong><\/p>\n\n\n\n<p>Dynamic programming is a methodology\nuseful for solving problems that involve taking decisions over several\nstages in a sequence. One thing common to all problems in this category is that\ncurrent decisions influence both present &amp; future periods. <\/p>\n\n\n\n<p><strong>SEQUENCING THEORY<\/strong><\/p>\n\n\n\n<p>It is related to Waiting Line Theory. It\nis applicable when the facilities are fixed, but the order of servicing\nmay be controlled. The scheduling of service or sequencing of jobs is done to\nminimize the relevant costs. <\/p>\n\n\n\n<p><strong>REPLACEMENT MODELS<\/strong><\/p>\n\n\n\n<p>These models are concerned with the\nproblem of replacement of machines, individuals, capital assets, etc.\ndue to their deteriorating efficiency, failure, or breakdown. <\/p>\n\n\n\n<p><strong>NETWORK SCHEDULING-PERT AND CPM<\/strong><\/p>\n\n\n\n<p>Network scheduling is a technique used\nfor planning, scheduling and monitoring large projects. Such large\nprojects are very common in the field of construction, maintenance, computer\nsystem installation, research and development design, etc. <\/p>\n\n\n\n<p><strong>INFORMATION THEORY<\/strong><\/p>\n\n\n\n<p>It is an analytical process transferred from the electrical communications field to operations research. It seeks to evaluate the effectiveness of information flow within a given system and helps in improving the communication flow.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"importance-of-operations-research\"><span class=\"ez-toc-section\" id=\"IMPORTANCE_OF_OPERATIONS_RESEARCH\"><\/span><strong>IMPORTANCE OF OPERATIONS RESEARCH<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Operations research is important because it is\na helpful tool used to solve complex problems under uncertainty. In business,\nvery few things are certain, and managers must often make decisions based on\ntheir instincts instead of being able to use reliable data. Operations research\ntechniques fill this void with methods that quantify issues and give business\nmanagers a better basis for making decisions.<strong><\/strong><\/p>\n\n\n\n<p><strong>IMPROVED DECISION MAKING<\/strong><\/p>\n\n\n\n<p>As the above example shows, operations\nresearch techniques can take a muddle of factors and numbers and reduce them to\nsimple formulas. These formulas will find the optimal solutions within the\nconstraints of the problem.<\/p>\n\n\n\n<p><strong>BETTER\nCONTROL<\/strong><\/p>\n\n\n\n<p>OR techniques give managers the tools that\nprovide better direction and control over subordinates. A manager can use OR\nmethods to set up performance standards for employees and identify areas that\nneed improvement.<\/p>\n\n\n\n<p><strong>HIGHER\nPRODUCTIVITY<\/strong><\/p>\n\n\n\n<p>A significant use of OR is the ability to\nidentify optimal solutions. A few examples are finding the best inventory mix,\noptimal utilization of manpower, most desirable use of plant machinery and\nhighest-producing marketing campaigns.<\/p>\n\n\n\n<p><strong>BETTER\nDEPARTMENTAL COORDINATION<\/strong><\/p>\n\n\n\n<p>When the optimal results from OR analysis are\nshared with all departments, everyone works together toward the same goal. For\nexample, the marketing department might coordinate their efforts with the\nschedules laid out by the production supervisor.<\/p>\n\n\n\n<p><strong>EFFECTIVE\nSYSTEMS<\/strong><\/p>\n\n\n\n<p>Operational research techniques are to analyze\nthe problem of decision making such as good site for plant, whether to open a\nnew storehouse, etc. It also helps in assortment of cost-effective means of\ntransportation, jobs sequencing, production scheduling, replacement of old\nmachinery, etc.<\/p>\n\n\n\n<p><strong>MAXIMIZE\nPROFITS &amp; MINIMIZE LOSSES<\/strong><\/p>\n\n\n\n<p>The operational Research techniques provide the\nquantitative data to take the decision which help the analyzer to take the\nappropriate decision which lead to maximize the profit and minimize the losses.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"role-of-operations-research-in-decision-making\"><span class=\"ez-toc-section\" id=\"ROLE_OF_OPERATIONS_RESEARCH_IN_DECISION_MAKING\"><\/span><strong>ROLE OF OPERATIONS RESEARCH IN DECISION MAKING<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Operations research plays an important role in\nalmost all areas of decision making. Some areas where operational research (OR)\ntechniques can be used as listed below: <\/p>\n\n\n\n<p><strong>FINANCING\nAND INVESTMENT POLICES<\/strong><\/p>\n\n\n\n<p>This category includes the analysis of credit and\nloan policy, fund flow and cash flow and also considers the dividend, share and\nbonus policy. It reflects the portfolio of investment too. <\/p>\n\n\n\n<p><strong>SELLING,\nPROMOTION, MARKETING &amp; PUBLICITY <\/strong><\/p>\n\n\n\n<p>It emphasis on selection of the product and\ntiming which means what type of commodity should be manufactured at the proper\npassage of the time. It focuses on the media of publicity like print media and\nelectronic media may be chosen. It also used to know about how many number of\nsales persons are required to some specific area. More over OR also use to\nselect the product mixed which include product, price, place and promotions. <\/p>\n\n\n\n<p><strong>ACQUISITION,\nINVESTIGATION, MANUFACTURING AND PERSONNEL MANAGEMENT <\/strong><\/p>\n\n\n\n<p>The operational research techniques being used to\npurchase, substitute and reorganize the most advantageous policies. These\ntechniques also include location and manufacturing size of retail outlets,\nfactories and warehouses, loading and unloading facilities for trucks,\nallocation and scheduling of resources and optimum to merge the products,\nrecruitment and selection of best suitable employee for a company and job\nassignments etc. <\/p>\n\n\n\n<p><strong>RESEARCH\nAND DEVELOPMENT <\/strong><\/p>\n\n\n\n<p>The methods currently available in literature for\nnumerically solving operational research problems may be broadly classified as\ndeterministic methods and probabilistic methods. The deterministic methods try\nto guarantee that a neighborhood of the solution of a problem is attained. Such\nmethods do not use any stochastic techniques, but rely on a thorough search of\nthe feasible domain. They are applicable, however, to a restricted class of\nproblems only. On the other hand the probabilistic methods make use of\nprobabilistic or stochastic approach to search for the solutions for the\nproblems. Although probabilistic methods do not give an absolute guarantee of\nthe exact solution having been obtained, these methods are sometimes preferred\nover the deterministic methods because they are applicable to wider class of\nproblems. <\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"limitations-of-operations-research\"><span class=\"ez-toc-section\" id=\"LIMITATIONS_OF_OPERATIONS_RESEARCH\"><\/span><strong>LIMITATIONS OF OPERATIONS RESEARCH<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>OR has some limitations. However, the limitations are\nrelated to the problem of model building and <\/p>\n\n\n\n<p>the time and money factors involved in application rather\nthan its practical utility. Some of them are <\/p>\n\n\n\n<p>as follows:<\/p>\n\n\n\n<p><strong>MAGNITUDE OF COMPUTATION<\/strong><\/p>\n\n\n\n<p>The models of OR strive to find out\noptimal solutions taking into account all the factors. These factors may\nbe huge and state them in quantity and establish relationships among the\nfactors require ample calculations which can be effectively solved by\ncomputers.<\/p>\n\n\n\n<p><strong>NON-QUANTIFIABLE FACTORS<\/strong><\/p>\n\n\n\n<p>OR provides solution only when all\nelements related to a problem can be quantified. All relevant variables\ndo not lend themselves to quantification. Factors which cannot be quantified\nfind no place in OR study. <\/p>\n\n\n\n<p><strong>DISTANCE BETWEEN USER AND ANALYST<\/strong><\/p>\n\n\n\n<p>OR being specialist\u2019s job requires a\nmathematician or statistician, who might not be aware of the business\nproblems. Similarly, a manager fails to understand the complex working of OR.\nThus there is a gap between the User and Analyst. <\/p>\n\n\n\n<p><strong>TIME AND MONEY COSTS<\/strong><\/p>\n\n\n\n<p>OR models are a costly proposition as\nthey require time and money for scientific application. The\ncomputational time increases depending upon the size of the problem and\naccuracy of results desired.<\/p>\n\n\n\n<p><strong>IMPLEMENTATION<\/strong><\/p>\n\n\n\n<p>Implementation of any decision is a\ndelicate task. It must take into account the complexities of human\nrelations and behavior. Sometimes, resistance is offered due to psychological\nfactors which may not have any bearing on the problem as well as its solution.<\/p>\n\n\n\n<p><strong>DIFFICULT TO BALANCE THE REQUIREMENT<\/strong><\/p>\n\n\n\n<p>It is often difficult to balance the\nrequirement of reality and those of simplicity.<\/p>\n\n\n\n<p><strong>POOR AND\/OR INACCURATE DATA<\/strong><\/p>\n\n\n\n<p>The quality of data collection may be\npoor and\/or inaccurate.<\/p>\n\n\n\n<p><strong>LACK OF SUITABLE SOLUTION TECHNIQUES<\/strong><\/p>\n\n\n\n<p>In many cases, the solution of Operations\nResearch problem is restricted by the lack of suitable solution\ntechniques. As example, the derived solution may be sub-optimal i.e. the\nboundaries of the problem may be open.<\/p>\n\n\n\n<p><strong>CONFLICT<\/strong><\/p>\n\n\n\n<p>An Operations Research model is static\nbut the solution it imitates is dynamics. Conflict between conclusion\nreached by the Operations Research analyst and the opinion of time managers as\nto the best course of action.<\/p>\n\n\n\n<p><strong>NOT A SUBSTITUTE FOR\nMANAGEMENT<\/strong><\/p>\n\n\n\n<p>Operations research only provides the tools and techniques\nand cannot be a substitute of management. It only examines the results of\nalternatives course of action and final decision is made by management within\nits authority and judgment. <\/p>\n\n\n\n<p><strong>SUB-OPTIMIZATION<br \/>\n<\/strong>Sub-optimization is deciding in respect of a relatively narrow aspect of\nthe whole business situation or optimization of a sub-section of the whole.\nFunctional heads sometimes, without taking care of wider implications,\nsub-optimize their functions. This may cause loss in that part of the\norganization which is left out of the exercise and as such should be avoided.<\/p>\n\n\n\n<p><strong>NOT REALISTIC<\/strong><\/p>\n\n\n\n<p>Operations research experts make very complex models for\nsolving problems. These models are\/ may not be realistic. Hence, they may not\nbe useful for real life situations.<\/p>\n\n\n\n<h3 class=\"has-text-align-center wp-block-heading\" id=\"conclusion\"><span class=\"ez-toc-section\" id=\"CONCLUSION\"><\/span><strong>CONCLUSION<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>The OR profession was for a time the centre of managerial attention. It had its golden era. It is now a small professional grouping which has found its niche. Few people realize that OR lies behind many every day events, providing the algorithms for airline reservation systems, checking the credit worthiness of loan applicants, and calculating the replenishment quantities required by supermarkets. Despite its important role in today\u2019s society OR lacks self-importance, it includes many, diverse interests and has demonstrated a certain capacity for survival.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Also Study<\/strong><\/td><td><strong>Also Study<\/strong><\/td><td><strong>Also Study<\/strong><\/td><\/tr><tr><td><a href=\"https:\/\/commerceiets.com\/operations-research\/\">Operations Research<\/a><\/td><td><a href=\"https:\/\/commerceiets.com\/linear-programming\/\">Linear Programming<\/a><\/td><td><a href=\"https:\/\/commerceiets.com\/assignment\/\">Assignment<\/a><\/td><\/tr><tr><td><a href=\"https:\/\/commerceiets.com\/linear-programming-problem\/\">Linear programming problems<\/a><\/td><td><a href=\"https:\/\/commerceiets.com\/linear-programming-applications\/\">Linear programming applications<\/a><\/td><td><a href=\"https:\/\/commerceiets.com\/linear-programming-applications\/\">Models of Operations research<\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link\" href=\"https:\/\/www.linkedin.com\/in\/kajal-mahajan-7549b2197\/\" target=\"_blank\" rel=\"noreferrer noopener\">CONNECT ON LINKEDIN<\/a><\/div>\n<\/div>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"266\" src=\"https:\/\/commerceiets.com\/wp-content\/uploads\/2019\/04\/cropped-Presentation-resize-1024x266.jpg\" alt=\"Operations Research\" class=\"wp-image-787\" srcset=\"https:\/\/commerceiets.com\/wp-content\/uploads\/2019\/04\/cropped-Presentation-resize-1024x266.jpg 1024w, https:\/\/commerceiets.com\/wp-content\/uploads\/2019\/04\/cropped-Presentation-resize-300x78.jpg 300w, https:\/\/commerceiets.com\/wp-content\/uploads\/2019\/04\/cropped-Presentation-resize-768x199.jpg 768w, https:\/\/commerceiets.com\/wp-content\/uploads\/2019\/04\/cropped-Presentation-resize-1536x398.jpg 1536w, https:\/\/commerceiets.com\/wp-content\/uploads\/2019\/04\/cropped-Presentation-resize.jpg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>OPERATIONS RESEARCH Operations research (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. The concept of OR arose during World War II by military planners. After the war,&#8230;<\/p>\n<p class=\"more-link-wrap\"><a href=\"https:\/\/commerceiets.com\/operations-research\/\" class=\"more-link\">Read More<span class=\"screen-reader-text\"> &ldquo;OPERATIONS RESEARCH FOR B.COM, BBA, M.COM &#038; MBA&rdquo;<\/span> &raquo;<\/a><\/p>\n","protected":false},"author":2,"featured_media":3319,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[228],"tags":[],"class_list":["post-3318","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-operations-research"],"_links":{"self":[{"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/posts\/3318","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/comments?post=3318"}],"version-history":[{"count":0,"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/posts\/3318\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/media\/3319"}],"wp:attachment":[{"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/media?parent=3318"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/categories?post=3318"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/commerceiets.com\/wp-json\/wp\/v2\/tags?post=3318"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}