Question

Define the followings:

a. Sensitivity Analysis

b. Sensitivity Analysis for Objective Function Coefficients

c. Sensitivity Analysis for Right Hand Side Values

d. Ranges of Optimality for Objective Function Coefficients

e. Ranges of Feasibility for Right Hand Side Values

f. Sensitivity Analysis by using QM for Windows

g. Sensitivity Analysis by using Excel

h. Shadow Price

Answer 1

Sensitivity Analysis: It is the variation in the output parameter due to deliberate changes made in input parameters that is objective function coefficients and right hand side values of constraints in order to study the effect of inputs on the output, predict the results or to get an idea of robustness of your model under uncertainty.

Sensitivity Analysis for Objective Function Coefficients: An objective function may have many variables with coefficients that may be required to be optimized to get a max or min over that function. Their increase or decrease one at a time, keeping others fixed, may determine its effect on the optimal basis to alter. Sensitivity Analysis for Objective Function Coefficients is varying such coefficients as input to objective function and analyzing its effect on optimal basis is Sensitivity Analysis for Objective Function Coefficients.

Sensitivity Analysis for Right Hand Side Values: An LP may have a number of constraints which necessarily affect the optimization of objective function. Carrying out a sensitivity analysis of right hand side parameters of constraints in order to see their effect on the output of the objective function is Sensitivity Analysis for Right Hand Side Values.

Ranges of Optimality for Objective Function Coefficients: It is maximum range {min,max} of permissible alteration to the objective function coefficients such that there is no change in the decision making, that is the decision variables remain optimal.

Ranges of Feasibility for Right Hand Side Values: Dual value is change in optimal solution per unit change in right hand side values of constraints. Range of feasibility is thus the the range over which dual value holds good and remain constant. Binding constraints which have potential to alter optimal solution needs to be handled properly.

Sensitivity Analysis Using QM for Windows

1. Select LP (Linear Programming ) Module
2. Select number of constraints.
3. Mention number of variables, the nature of variables. Its mandatory to declare if the some of them are non negative, integers etc.
4. Select if the objective function is required to be maximized and minimized.

5. After obtaining the results, use sensitivity analysis option provided by windows to get more information.

Sensitivity Analysis by using Excel:

1. Get results for your optimization problem using excel solver
2. Prepare data table for results.
3. Use WHAT-IF Analysis for sensitivity analysis.

Shadow Price: It is change in the optimal solution when right hand side value is changed by unity. It is a term related to each constraints. It may be positive, negative or a zero. Its valid for permissible change in a given constraint. A sensitivity analysis for Shadow Price gives information about how the optimality changes if RHS is changed in allowed range.