Business & Economics

Assignment on Operations Research

ASSIGNMENT ON OPERATIONS RESEARCH ASSIGNMENT ON OPERATIONS RESEARCH BY RAHUL GUPTA Q.1: Describe in details the OR approach of problem solving. What are the limitations of the Operations Research? Answer:  OR approach of problem solving: Optimization is the act of obtaining the best result under any given circumstance. In various practical problems we may have to take many technical or managerial decisions at several stages. The ultimate goal of all such decisions is to either maximize the
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  ASSIGNMENT ON OPERATIONS RESEARCH ASSIGNMENT ONOPERATIONSRESEARCHBY RAHUL GUPTA Q.1: Describe in details the OR approach of problem solving. Whatare the limitations of the Operations Research? Answer:   OR approach of problem solving: Optimization is the act of obtaining the best result under any given circumstance. Invarious practical problems we may have to take many technical or managerial decisionsat several stages. The ultimate goal of all such decisions is to either maximize thedesired benefit or minimize the effort required. We make decisions in our every day lifewithout even noticing them. Decision-making is one of the main activities of a manager or executive.In simple situations decisions are taken simply by common sense, sound judgmentand expertise without using any mathematics. But here the decisions we are concernedwith are rather complex and heavily loaded with responsibility. Examples of such RAHUL GUPTA, MBAHCS (2 ND SEM), SUBJECT CODE-MB0032, SET-2Page 1  ASSIGNMENT ON OPERATIONS RESEARCH decision are finding the appropriate product mix when there are large numbers of  products with different profit contributions and production requirement or planning public transportation network in a town having its own layout of factories, apartments, blocks etc. Certainly in such situations also decision may be arrived at intuitively fromexperience and common sense, yet they are more judicious if backed up bymathematical reasoning.The search of a decision may also be done by trial and error but such a search may be cumbersome and costly. Preparative calculations may avoid long and costly research.Doing preparative calculations is the purpose of Operations research. Operationsresearch does mathematical scoring of consequences of a decision with the aim of optimizing the use of time, efforts and resources and avoiding blunders.The application of Operations research methods helps in making decisions in suchcomplicated situations. Evidently the main objective of Operations research is to provide a scientific basis to the decision-makers for solving the problems involving theinteraction of various components of organization, by employing a team of scientistsfrom different disciplines, all working together for finding a solution which is the bestin the interest of the organization as a whole. The solution thus obtained is known asoptimal decision.  Features of Operations Research: ã It is System oriented :OR studies the problem from over all points of view of organizations or situations since optimum result of one part of the system may not be optimum for someother part.ã It imbibes Inter – disciplinary team approach: Since no single individual can have a thorough knowledge of all fast developingscientific know-how, personalities from different scientific and managerial cadre form ateam to solve the problem. RAHUL GUPTA, MBAHCS (2 ND SEM), SUBJECT CODE-MB0032, SET-2Page 2  ASSIGNMENT ON OPERATIONS RESEARCH ã It makes use of Scientific methods to solve problems.ãOR increases the effectiveness of a management Decision making ability.ãIt makes use of computer to solve large and complex problems.ãIt gives Quantitative solution.ãIt considers the human factors also. The first and the most important requirement is that the root problem should be identifiedand understood. The problem should be identified properly, this indicates three major aspects: ã A description of the goal or the objective of the study. ã An identification of the decision alternative to the system. ã Recognition of the limitations, restrictions and requirements of the system.  Limitations of OR: The limitations are more related to the problems of model building, time and money factors. ã Magnitude of computation: Modern problem involve large number of variables andhence to find interrelationship, among makes it difficult. ã  Non – quantitative factors and Human emotional factor cannot be taken into account. ã There is a wide gap between the managers and the operation researches. ã Time and Money factors when the basic data is subjected to frequent changes thenincorporation of them into OR models are a costly affair. ã Implementation of decisions involves human relations and behavior  Q 2: What are the characteristics of the standard form of L.P.P.? What is the standard form of L.P.P.? State thefundamental theorem of L.P.P? Answer:  Introduction: RAHUL GUPTA, MBAHCS (2 ND SEM), SUBJECT CODE-MB0032, SET-2Page 3  ASSIGNMENT ON OPERATIONS RESEARCH Inmathematics, linear programming (LP) is a technique for optimizationof alinear   objective function, subject tolinear equalityandlinear inequality constraints. Informally, linear   programming determines the way to achieve the best outcome (such as maximum profit or lowest cost) in a givenmathematical modeland given some list of requirements represented aslinear equations.More formally, given a polyhedron(for example, apolygon), and areal-valuedaffine  functiondefined on this polyhedron, a linear programming method will find a point onthe polyhedron where this function has the smallest (or largest) value if such pointexists, by searching through the polyhedron vertices.Linear programs are problems that can be expressed incanonical form:MaximizeSubject toRepresents the vector of variables (to be determined), while and are vectors of (known)coefficients and is a (known) matrix of coefficients. The expression to be maximized or minimized is called the objective function ( in this case). The equations are theconstraints which specify aconvex polytopeover which the objective function is to be optimized.Linear programming can be applied to various fields of study. Most extensively it isused in business and economic situations, but can also be utilized for some engineering problems. Some industries that use linear programming models include transportation, energy,telecommunications, and manufacturing. It has proved useful in modeling diverse types of  problems in planning, routing, scheduling, assignment, and design. Uses : Linear programming is a considerable field of optimization for several reasons. Many practical problems inoperations researchcan be expressed as linear programming problems.Certain special cases of linear programming, such as network flow problems and multicommodity flow problems are considered important enough to have generated much research on RAHUL GUPTA, MBAHCS (2 ND SEM), SUBJECT CODE-MB0032, SET-2Page 4
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