
BITS Operations Research SemVI Unit 1 : Linear Programming(Mathematical formulation of the problem, Graphical solution, The simplex method, Charnes method of penalties, Concept of duality, Dual simplex method) 


1. Operations Research(Computer Science) 
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Introduction, Linearprogramming1, LPâ€" 2, Simplex Method, Simplex Methodâ€" 2, Simplex Methodâ€" 2, Duality Theory, Duality Theory and Sensitivity Analysis, Other Algorithms for LP, Transportation and Assignment Problems, Game Theory, Decision Analysis, Metahuristics
Title: Operations Research




2. Introduction, Linearprogramming1, LPÃ¢â‚¬â€œ 2, Simplex Method1, Simplex Method 2, Duality Theory, Duality Theory and Sensitivity Analysis, Other Algorithms for LP, Transportation and Assignment Problems, Game Theory, Decision Analysis, Metahuristics(Computer Science) 
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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). Another term which is used for this field is "management science" ("MS"). The Americans
sometimes combine the terms OR and MS together and say "OR/MS" or "ORMS".Yet other terms sometimes used are "industrial engineering" ("IE"),
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Title: Operations Research




3. Duality Theory and Sensitivity Analysis, Algorithms for LP(Operations Research (computer Science and Information Science Engineering)) ) 
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Introduction, The Role of Duality Theory in Sensitivity Analysis, The Essence of Sensitivity Analysis, Applying Sensitivities Analysis, Dual Simplex Method, Parametric Linear Programming, Integer Programming, The Upper Bound Technique (Branch and Bound Method).
Title: Introduction to operations Research




4. Duality(Operation Research) 
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Associated with every linear programming problem there is another intimately related problem, called the dual problem of the original LP problem. The original LP problem is called the primal problem. According to the duality theorem:" For every maximization (or minimization) problem in linear programming, there is a unique similar problem of minimization (or maximization) involving the same data w
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Title: MB115 Operations Research




5. Simplex Method  2, Duality Theory(Operations Research (computer Science and Information Science Engineering)) ) 
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Introduction, Fundamental Insight, Revised Simplex Method, The Essence of Duality Theory (Concept of Duality), Primal Dual Relationship  Adopting Other Primal Forms.
Title: Introduction to operations Research




6. Primal and Dual Problem(Operations Research
) 
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Associated with every linear programming problem there always exists another programming problem which is based upon the same data and having the same solution. The original problem is called the primal problem while the associated one is called its dual problem. From both the theoretical and practical points of view, the theory of duality is one of the most important and interesting concepts in l
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Title: Optimization In Engineering




7. Concept of Linear Programming Model(Mathematics) 
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To constitute on development of the specific Operational research techniques to determine the optimal choice among several courses of Operations, including the evaluation of specific numerical values we need to construct (formulate) a mathematical model. LP had its beginning in the inputoutput analysis developed by the well known economist W. W. Leontief. Hitchcock and Koopman's transportation ty
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Title: Math 2.5 Operations Research




8. Introduction to or & Linear Programming(Operation Research) 
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Operations research is a new branch of mathematics dealing with the optimization problems in reallife situations. It is also a quantitative technique to deal many management problems. In this discipline. We study cost minimization of various inventory problems, the minimization of transportation costs of sending goods from various warehouses to different centers. the profit maximization or cost m
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Title: MB115 Operations Research




9. Method for Optimal Solution(Operations Research
) 
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Linear programming methods solve optimization problems having linear objective function and constraints. That is why this methods are extensively in operations research or transportation problem. Linear programming methods can also solve problems having some particular types of nonlinear objective function and linear constraints which is explained in chapter 10.
Title: Optimization In Engineering




10. Integer Programing(Operations Research
) 
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In mathematical programming problems, some times the value of the
results comes out to be negative and fraction. In such cases the solution
is not optimal. In linear programming it is assumed that the decision
variables can take continuous values that is, these could be fractions or
integers. Integer programming deals with solutions where some or all
the variables can assume integers nonnega
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Title: Operations Research




11. Introduction(Operations Research
) 
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Operations Research (OR) is an art and science concerned with the
efficient allocation/utilization of scarce resources. The art lies in the
ability to depict concepts of efficiency and scarcity in a welldefined
mathematical model for a given situation. The science consists in the
derivation of computational methods for solving such models.
Title: Operations Research




12. Introduction, Linear Programming  1(Operations Research (computer Science and Information Science Engineering)) ) 
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Introduction, Definitions of Operations Research, Origin of Operations Research (Historical Development), Impact of Operations Research (Applications), Defining the Problem and Gathering Data (Phases of OR), Mathematical Model of OR Testing the Model , , Nature of OR (Features of OR), Limitations of OR Models, Introduction to Linear Programming, Graphical Method.
Title: Introduction to operations Research





13. Integer Programming Problem(Operations Research
) 
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A linear programming problem in which all or some of the decision variables are constrained to some nonnegative integer values is called an integer programming problem. This type of problem is of particular importance in business and industry where, quit often, the fractional solutions are unrealistic because the units are not divisible.
Title: Optimization In Engineering




14. Solution of Linear Programming Problems(Operations Research
) 
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Graphical method used to solve a Linear Programming Problem is limited
to two decision variable problems. But most real life problems when formulated as LP model will have more than two decision variables.
Thus, we need a more efficient method to suggest an optimal solution of such problems. A more general method known as "Simplex Method" is suitable for solving Linear Programming Problems with
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Title: Operations Research




15. Optimization(Mathematics III) 
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In this chapter, we introduce some basic notions of the Optimization Theory which deals with the act of obtaining best results under given circumstances. Linear programming is an important topic in the optimization theory, and our discussion is confined to an elementary exposition of this topic.
Title: Engineering Mathematics Part  III




16. Linear Programming Problem  Simplex Method(Operations Research (Mechanical and Allied Streams of VTU)) 
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Introduction, Standard Form of a LP Problem (Characteristics of LPP), Steps in Simplex Method, Artificial Variables, Dual Simplex Method, Degeneracy in LPP.
Title: Introduction to operations Research




17. Introduction to Operations Research(Computer Science) 
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Operations research is the application of scientific method by interdisciplinary teams to problems involving the control of organized (manmachine) systems so as to provide solutions which best serve the purpose of the organization as a whole
Title: Operations Research
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18. Solution to Linear Programming Problems(Mathematics) 
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In the last section, we've discussed the formulation of LPP and existence of different types of solutions and the nature of the solutions. In this section, we've solved the LPP problems by describing different methods. In particular, we concentrate on the following methods. Graphical method, Simplex method, Big••M method, Dual Simplex method and Two  Phase Simplex method. All the above
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Title: Math 2.5 Operations Research




19. Integer Programming(Operations Research (Mechanical and Allied Streams of VTU)) 
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Introduction, Formulation of Integer Programming, Methods of Integer Programming, Cutting Plane Algorithm, Branch and Bound Method, Limitations of Integer Linear Programming, Zero One Algorithm.
Title: Introduction to operations Research




20. Linear Programming  2, Simplex Method  1(Operations Research (computer Science and Information Science Engineering)) ) 
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Introduction, Basic Terms / Definitions, Standard Form of a LP Problem, (Characteristics of LPP), The Setting up and Algebra of Simplex Method, Steps of Simplex Method in Brief, Tie Breaking in Simplex Method (Degeneracy), Unbounded Solution, Multiple Optimal Solution.
Title: Introduction to operations Research




21. Transportation Problems(Operations Research
) 
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The aim of transportation problem is to transport various amounts of a single homogeneous commodity, which are initially stored at various origins, to different destinations in such a way that the total transportation cost is minimum.
Title: Operations Research




22. Introduction(Operations Research
) 
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Operation Research abbreviated as OR may be described as a scientific approach to decision making. The term operations research was first coined in 1940 by Mc Closky and Trefthen in Bowdsey of the United Kingdom. This new science came into existence during the second world war of 193945. At that time, the military management in England called upon a team of scientists to study the strategic and t
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Title: Operations Research





23. Introduction of Scientific Research and Good Scientific Practices (GSP)(Clinical Nutrition and Dietetics) 
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The scientific enterprise is built on a foundation of trust. Society trusts that scientific research results are an honest and accurate reflection of a researcher's work. Researchers equally trust that their colleagues have gathered data carefully, have used appropriate analytic and statistical techniques, have reported their results accurately, and have treated the work of other researchers with
......
Title: MSc.CND103 Research Methods and Biostatistics




24. Linear Programming(Operations Research
) 
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Many management decisions are concerned with the problem of planning activity. In each case, there will be limited resources and it becomes necessary to utilize these resources so as to yield maximum production or to minimize the cost of production, or to give maximum profits etc. Such problems are referred to as the problems of constrained optimization. Linear programming is a mathematical modeli
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Title: Operations Research





25. Linear Programming(Mathematics) 
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Mathematical Formulation of LPP, Solution of LPP by Graphical Method, Solution of LPP by Simplex Method.
Title: Introductory Mathematics IV






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