How can I apply sensitivity analysis to optimize a linear programming model?

Sensitivity analysis is a powerful tool for optimizing linear programming models. Here's how you can apply it effectively:

1. Shadow Prices: Analyze the shadow prices (dual variables) associated with each constraint. Higher shadow prices indicate constraints that have a greater impact on the objective function.
2. Reduced Costs: Examine the reduced costs for non-basic variables. Variables with small reduced costs are candidates for entering the basis and potentially improving the solution.
3. Allowable Increases/Decreases: Calculate the range within which coefficients can change without affecting the optimal solution. This helps identify which parameters are most sensitive.
4. Parametric Programming: Systematically vary key parameters and observe how the optimal solution changes. This can reveal critical thresholds and relationships.
5. Monte Carlo Simulation: For more complex models, use Monte Carlo methods to simulate various scenarios and identify key drivers of the solution.

Tools like Excel's Solver, LINDO, or more advanced software like CPLEX can assist in performing these analyses.

For further reading, I recommend the following resource:
Sensitivity analysis in linear programming and semidefinite programming using interior-point methods