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Linear Programming: Computer Solution and Sensitivity Analysis - Coggle…
Linear Programming: Computer Solution and
Sensitivity Analysis
Definition
Mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for a system.
Utilizes linear relationships to represent constraints and objectives
Computer Solution
Algorithm Implementation
Various algorithms like Simplex Method, Interior Point Method, and others are used for solving linear programming problems.
Software Tools
Dedicated software packages like CPLEX, Gurobi, and MATLAB are commonly employed for solving linear programming problems efficiently
Sensitivity Analysis
Definition
Examination of how the optimal solution of a linear programming problem changes as parameters in the model vary.
Key Aspects
Changes in objective function coefficients
Changes in constraint coefficients
Changes in right-hand side values of constraints.
Purpose
Helps in understanding the robustness of the solution and provides insights into decision-making under uncertainty.
Integration of Computer Solution and Sensitivity Analysis
Iterative Process
Solve the linear programming problem using computer algorithms.
Conduct sensitivity analysis to evaluate the impact of changes in parameters.
Refine the solution based on the analysis results if necessary.
Optimization
Use sensitivity analysis findings to optimize the solution further, improving decision-making and resource allocation.
Applications
Business and Finance
Optimal resource allocation, production planning, portfolio optimization.
Engineering
Supply chain management, network design, project scheduling.
Healthcare
Healthcare resource allocation, treatment planning.
Environmental Management
Pollution control, waste management, sustainable resource utilization.
Background Competencies
Linear programming, coupled with computer solution techniques and sensitivity analysis, provides powerful tools for optimizing decision-making processes across various domains. Understanding these concepts and their applications is essential for efficient resource allocation and problem-solving
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