Understanding Sensitivity Analysis in Linear Programming

Sensitivity Analysis: The study of how changes in the coefficients of a linear programming problem affect the optimal solution.

Objective Function Coefficient Allowable Increase (Decrease): The allowable increase (decrease) of an objective function coefficient is the amount the coefficient may increase (decrease) without causing any change in the values of the decision variables in the optimal solution. The allowable increase/decrease for the objective function coefficients can be used to calculate the range of optimality.

Objective Coefficient Range (Range of Optimality): The range of values over which an objective function coefficient may vary without causing any change in the values of the decision variables in the optimal solution.

Shadow Price: The change in the optimal objective function value per unit increase in the right-hand side of a constraint.

Reduced Cost: If a variable is at its lower bound of zero, the reduced cost is equal to the shadow price of the non-negativity constraint for that variable. In general, if a variable is at its lower or upper bound, the reduced cost is the shadow price for that simple lower or upper bound constraint.

Range of Feasibility: The range of values over which the shadow price is applicable.

Right-Hand-Side Allowable Increase (Decrease): The allowable increase (decrease) of the right-hand side of a constraint is the amount the right-hand side may increase (decrease) without causing any change in the shadow price for that constraint. The allowable increase and decrease for the right-hand side can be used to calculate the range of feasibility for that constraint.

Sunk Cost: A cost that is not affected by the decision made. It will be incurred no matter what values the decision variables assume.

Relevant Cost: A cost that depends upon the decision made. The amount of a relevant cost will vary depending on the values of the decision variables.

1. Six steps typically taken in applied regression analysis for a given dependent variable are:

• Review the literature and develop the theoretical model.
• Specify the model: Select the independent variables and the functional form.
• Hypothesize the expected signs of the coefficients.
• Collect the data. Inspect and clean the data.
• Estimate and evaluate the equation.
• Document the results.

2. A dummy variable takes on only the values of 1 or 0, depending on whether some condition is met. An example of a dummy variable would be X equals 1 if a particular individual is female and 0 if the person is male.