Sensitivity Analysis Flashcards
What is Sensitivity Analysis in Linear Programming?
Sensitivity analysis examines how the optimal solution to an LP problem might change in response to variations in the input data (parameters of the model).
Why is Sensitivity Analysis important?
It helps determine the impact of changes in model parameters, accommodating real-world uncertainties and providing insight into the stability of the solution.
What is the sensitivity range for an objective function coefficient?
It is the range of values for which the current optimal solution remains optimal, even as the coefficient changes.
What happens if the objective function coefficient changes within its sensitivity range?
The optimal solution remains unchanged, although the optimum objective value may change.
What are the steps if a coefficient change is outside the sensitivity range?
The simplex method is used to recompute the z-row and recover optimality.
What is the RHS sensitivity range?
It indicates how much the RHS value of a constraint can change without altering the optimal solution’s variable mix, including slack variables.
What happens when the RHS of a constraint changes within its sensitivity range?
The basis remains unchanged, meaning the solution remains optimal and feasible.
How does changing the RHS value of a labor constraint affect an LP solution?
It alters the available resources, potentially affecting the optimal production levels in manufacturing scenarios, like in the Pottery example.
What are shadow prices in Sensitivity Analysis?
They represent the change in the objective function’s value per unit increase in the RHS value of a constraint, holding other problem data constant.
What does a change in the objective function’s coefficients imply for decision-making?
It affects the profitability or cost associated with each decision variable, necessitating a reevaluation of resource allocation strategies.
Does adding a constant to the objective function change the optimal solution?
No, it does not affect the optimal solution.
Does scaling the objective function’s coefficients alter the optimal solution?
No, scaling the coefficients does not change the optimal solution but changes the scale of the objective value.
What effect does reordering decision variables have on the optimal solution?
Reordering the decision variables along with their respective coefficients does not change the optimal solution.
