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Operations Research Book by Kanti Swarup Free 97: How to Learn the Science of Decision Making

Operations research is a branch of mathematics that deals with the analysis and optimization of complex systems and processes. It involves using mathematical models, algorithms, and techniques to find the best solutions for various problems in business, engineering, management, and other fields. Operations research can help you make better decisions, improve efficiency, reduce costs, and increase profits.

If you are interested in learning operations research, you might want to check out the book Operations Research by Kanti Swarup, P.K. Gupta, and Manmohan. This book is a comprehensive and accessible introduction to the subject, covering topics such as linear programming, transportation problems, assignment problems, game theory, inventory models, queuing theory, simulation, network analysis, dynamic programming, and more. The book also includes numerous examples, exercises, and case studies to illustrate the concepts and applications of operations research.

But what if you don’t have the money or the time to buy or read the book? Don’t worry, there is a way to get it for free and learn 97 essential concepts of operations research. Here’s how:

How to Download Operations Research Book by Kanti Swarup for Free

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How to Learn 97 Essential Concepts of Operations Research

Now that you have downloaded Operations Research Book by Kanti Swarup for free, you might be wondering how to learn 97 essential concepts of operations research from it. The book has 891 pages and 32 chapters, so it might seem overwhelming at first. However, you don’t have to read the whole book to learn the basics of operations research. You can focus on some key chapters and topics that cover the most important concepts and techniques.

Here are some suggestions on how to learn 97 essential concepts of operations research from Operations Research Book by Kanti Swarup:

• Read Chapter 1: Introduction to Operations Research. This chapter will give you an overview of what operations research is, what are its objectives and scope, what are its applications and limitations, and what are its phases and methodology.
• Read Chapter 2: Linear Programming Problems (LPP). This chapter will introduce you to one of the most fundamental and widely used tools of operations research: linear programming. You will learn what is a linear programming problem, what are its assumptions and characteristics, how to formulate it mathematically, how to solve it graphically and algebraically using the simplex method, how to interpret the optimal solution and its sensitivity analysis.
• Read Chapter 3: Duality in Linear Programming. This chapter will explain another important concept in linear programming: duality. You will learn what is duality theory, what are its benefits and applications, how to derive the dual problem from the primal problem, how to solve it using the dual simplex method or complementary slackness theorem.
• Read Chapter 4: Transportation Problems (TP). This chapter will teach you how to apply linear programming to solve transportation problems. You will learn what is a transportation problem, how to formulate it as a linear programming problem, how to find an initial basic feasible solution using various methods such as north-west corner rule or Vogel’s approximation method (VAM), how to test for optimality using stepping stone method or modified distribution method (MODI), how to deal with degeneracy or unbalanced problems.
• Read Chapter 5: Assignment Problems (AP). This chapter will show you how to apply linear programming to solve assignment problems. You will learn what is an assignment problem,

  What is an Assignment Problem?

  An assignment problem is a special type of linear programming problem where the objective is to assign a number of resources to an equal number of tasks so as to minimize the total cost or maximize the total profit of the assignment. For example, you might want to assign workers to machines, salesmen to territories, jobs to machines, etc.

  An assignment problem can be represented by a cost matrix, where each row corresponds to a resource, each column corresponds to a task, and each element represents the cost or profit of assigning that resource to that task. For example, the following table shows the cost matrix of assigning four workers to four machines:

  	Machine 1	Machine 2	Machine 3	Machine 4
  Worker 1	10	12	9	11
  Worker 2	8	9	7	6
  Worker 3	9	10	12	8
  Worker 4	11	13	10	9

  The problem is to find an optimal assignment that minimizes the total cost of assigning four workers to four machines.

  How to Solve an Assignment Problem?

  One of the most efficient methods for solving an assignment problem is the Hungarian method, which was developed by Kuhn (1956) and Flood (1956) based on theorems proved by Hungarian mathematicians König (1950) and Egerváry (1953). The Hungarian method works on the principle of reducing the given cost matrix to a matrix of opportunity costs, where each row and column has at least one zero element. Then, it uses a systematic procedure to find an optimal assignment that covers all the zero elements.

  The Hungarian method can be summarized in the following steps:

  1. Determine the smallest element in each row of the given cost matrix and subtract it from every element of that row.
  2. Determine the smallest element in each column of the reduced matrix obtained in step 1 and subtract it from every element of that column.
  3. Determine the minimum number of horizontal and vertical lines required to cover all the zero elements in the reduced matrix obtained in step 2. If this number is equal to the order of the matrix (the number of rows or columns), then an optimal assignment is possible and go to step 5. Otherwise, go to step 4.
  4. Determine the smallest element among all the uncovered elements in the reduced matrix obtained in step 2 and subtract it from every uncovered element. Then, add this element to every element that is covered by two lines. Repeat step 3.
  5. Determine an optimal assignment by selecting one zero element from each row and column such that no two selected elements belong to the same row or column. The total cost or profit of this assignment is equal to the sum of all the elements that were subtracted or added during the reduction process.

  Conclusion

  Operations research is a branch of mathematics that deals with the analysis and optimization of complex systems and processes. It can help you make better decisions, improve efficiency, reduce costs, and increase profits in various fields. One of the best books to learn operations research is Operations Research by Kanti Swarup, P.K. Gupta, and Manmohan. This book covers topics such as linear programming, integer programming, non-linear programming, network modeling, inventory theory, queueing theory, decision theory, game theory, dynamic programming, and Markov processes. You can get this book for free from Scribd and learn 97 essential concepts of operations research from it. You can also use some specific methods to solve transportation problems, which are a special type of linear programming problems that deal with minimizing the cost of transporting a commodity from sources to destinations.

  We hope this article has helped you understand the basics of operations research and how to get and use Operations Research Book by Kanti Swarup for free. If you want to learn more about operations research and its applications, you can check out some of the following resources:

  • Operations Research: An Introduction by Hamdy A. Taha
  • Introduction to Operations Research by Frederick S. Hillier and Gerald J. Lieberman
  • Operations Research: Applications and Algorithms by Wayne L. Winston
  • Operations Research: A Textbook for Students of Mathematics, Statistics Commerce, Engineering and Management of All Indian Universities by Kanti Swarup, P.K. Gupta – Google Books
  • Operations Research/Transportation and Assignment Problem – Wikibooks
  • Operations Research for Transportation and Sustainable Development – Journal of Advanced Transportation
  • Transportation Problem in Operational Research – GATEXplore
  • Comparison of Transportation Problem in Operation Research – IJRASET

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