Question

(a) What do you understand by sensitivity analysis? Why is it important? How can you use the sensitivity ranges to decide whether your recommendations based on the optimal solution of a linear programming problem are robust or not?

(b) What is an assignment problem? Briefly discuss the decision variables, the objective function and the constraint requirements in an assignment problem. How do we determine whether a given assignment problem is balanced? Give a real-world example of the assignment problem.

(c) What is a diet problem? Briefly discuss the decision variables, the objective function and the constraint requirements in a diet problem. Give a real-world example of a diet problem.

(d) What is the required format of a linear programming problem needed if we want to solve it by using QM for Windows? What information about the solution can you collect from the results provided by QM for Windows? Discuss briefly

Answer 1

a)

Sensitivity analysis is the report that shows the sensitivity of the objective function to the constraints and coefficient of decision variables. It is a detailed report that shows the sensitive ranges for optimum solution and other details such as surplus and slack of the constraint RHS.

The importance of sensitivity analysis can be often seen in the real world. For example, it helps us to understand the resources which are more valuable and attempt to optimize our resource utilization further. For example, if a resource constraint is a binding constraint then we may try to reduce non-binding constraints and increase the binding constraint to increase the value of our objective function.

Linear programming usually shows the robust solution on the sensitivity analysis. However, if there are rooms for adjustment to the constraints and coefficient of decision variable, then the overall solution can be further optimized by using the ranges.