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.

Various algorithms like Simplex Method, Interior Point Method, and others are used for solving linear programming problems.

Utilizes linear relationships to represent constraints and objectives

Dedicated software packages like CPLEX, Gurobi, and MATLAB are commonly employed for solving linear programming problems efficiently

Examination of how the optimal solution of a linear programming problem changes as parameters in the model vary.

Helps in understanding the robustness of the solution and provides insights into decision-making under uncertainty.

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.

Use sensitivity analysis findings to optimize the solution further, improving decision-making and resource allocation.

Optimal resource allocation, production planning, portfolio optimization.

Supply chain management, network design, project scheduling.

Healthcare resource allocation, treatment planning.

Pollution control, waste management, sustainable resource utilization.

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