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Linear Programming by Robert J. Vanderbei Book Details
| Book Name | Linear Programming |
| Author | Robert J. Vanderbei |
| Category | Computer Science Books, Software Engineering Books, Tech & Computer Books, Education Books |
| Book Language | English |
| Pages | 420 |
| Country | India |
| Book Size | 5 MB |
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About Linear Programming by Robert J. Vanderbei Book
Linear programming (LP) is a mathematical optimization technique used to find the best possible solution to a problem involving linear constraints and a linear objective function. It is widely applied in various fields, including operations research, economics, engineering, and management, to make optimal decisions in resource allocation, production planning, transportation, finance, and more.
Here are the key components and concepts of linear programming:
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Decision Variables: These are the quantities that need to be determined to optimize the objective function. They represent the choices or decisions you're trying to make.
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Objective Function: The objective function is a linear mathematical expression that needs to be maximized or minimized. It typically represents a measure of success, such as profit, cost, time, or utility.
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Constraints: Constraints are limitations or restrictions on the decision variables. These can include limitations on resources, capacities, budgets, or other factors.
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Feasible Region: The feasible region is the set of all possible combinations of decision variables that satisfy all the constraints.
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Optimal Solution: The optimal solution is the combination of decision variables within the feasible region that maximizes (or minimizes) the objective function.
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Linear Equations and Inequalities: Linear programming problems involve linear equations and inequalities. The objective function and constraints are linear expressions.
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Graphical Method: In some cases, linear programming problems can be solved graphically by plotting constraints and identifying the corner points of the feasible region.
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Simplex Method: The simplex method is a widely used algorithm for solving linear programming problems by iteratively moving along the edges of the feasible region to reach the optimal solution.
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Dual Problem: Linear programming has a dual problem associated with it, which provides insights into the shadow prices of constraints and can be useful for sensitivity analysis.
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Sensitivity Analysis: Linear programming allows you to analyze how changes in parameters (coefficients, constraints, etc.) affect the optimal solution and objective function values.
Linear programming is a versatile tool that can address a wide range of optimization problems. It has been used to optimize production schedules, distribution networks, investment portfolios, transportation routes, and more. The technique's effectiveness lies in its ability to provide systematic and quantifiable solutions to complex decision-making problems involving limited resources and multiple objectives.
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