Understanding basic principles of decision-making.
| Chapter No. | Chapter Name | Key Topics Covered | | :--- | :--- | :--- | | 1 | Linear Programming Problems | Introduction to LPP, problem formulation, and mathematical modeling | | 2 | Features of Optimal Solutions | Understanding the nature and characteristics of optimal solutions | | 3 | Mathematical Preliminaries | Review of necessary mathematical concepts, including convexity theory | | 4 | Simplex Method | The core algorithm for solving linear programming problems | | 5 | Degeneracy | A special case in LP where the simplex method may cycle | | 6 | Duality | The concept of primal and dual problems and their relationship | | 7 | Dual Simplex Method | A variant of the simplex method used for certain types of LP problems | | 8 | Transportation Problems | A special class of LP for efficiently moving goods from sources to destinations | | 9 | Assignment Problems | A specialized LP problem for optimally assigning tasks to agents | | 10 | Geometrical Aspects of Optimal Solutions | Visualizing LP solutions in geometric space | | 11 | Sensitivity Analysis | Studying how changes in model parameters affect the optimal solution | | 12 | Integral Linear Programming | Also known as Integer Programming, where solutions must be whole numbers | | 13 | Game Theory | The formal study of strategic decision-making among conflicting parties | | Appendix A | General Mathematical Programming Problems | Additional problems for practice | | Appendix B | Some Advanced Linear Programming Topics | A look at more sophisticated concepts in the field |
To demonstrate the mathematical duality that links optimization and games. 2. Core Concepts in Linear Programming (LP) Linear Programming And Game Theory Ghosh Chakraborty Pdf
The unknowns that need to be determined (e.g., quantities of products to produce).
When no saddle point exists, players must assign probabilities to their choices to keep their opponents guessing. Graphical and Algebraic Solutions Understanding basic principles of decision-making
: A set of linear inequalities or equations that represent restriction limits (e.g., available labor hours or raw materials). Standard Methods of Solution
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A systematic, algebraic method for solving complex LPPs.
Chapters feature a wide array of solved examples followed by unsolved problems to test comprehension.
Comprehensive Guide to Linear Programming and Game Theory by Ghosh and Chakraborty