Need help in interpreting the sensitivity analysis. Acme Chemical rate of investment can change between 8.65% and 8.75% (Allowable increase and decrease)
Similarly, Abhishek Corp can vary between 9.25% and 10%.
However, the reduced cost value is 0.00% which is contrary to the ranges since reduced cost being 0, indicates that even a 0.1% change in interest rates would change the optimal solution.
On
Two things I am not sure about in the Sensitivity Report. One some of the variants have positive values and still has a reduced cost. In an optimal solution, the only reduced cost that you should be concerned is the one which has for it a zero value. and then the definition of reduced cost kicks in. For the first two, reduced cost of 0 means they are already positive and the change in the objective coefficient to allowable decrease or increase to make the variant positive is meaningless.
These are the excerpts from a lecture at Ohio State University.
If, at an optimal solution, a variable has a positive value, the reduced cost for that variable will be 0.
If, at an optimal solution, a variable has a value of 0, the reduced cost for that variable can be interpreted as the amount by which the objective value will change if we increase the value of this variable to one, assuming a feasible solution still exists.
If, at an optimal solution, a variable has a value of 0, the reduced cost for that variable can also be interpreted as the amount by which the objective coefficient would have to decrease in order to have a positive value for that variable in an optimal solution.
The confusion about ranges and zero reduced costs might have to do with the fact that, in a basic feasible solution, the values of the basic variables are uniquely determined by the values of the nonbasic variables. A nonzero reduced cost (on a nonbasic variable) tells you what would happen to the objective value if you forced that nonbasic variable to move off whichever bound (lower or upper) it currently sits on. So for Balaji (nonbasic on its lower bound), forcing a small investment in Balaji reduces the overall yield by 0.25% times that investment, while for Amar (nonbasic on its upper bound), forcing the solution to invest a little less in Amar would reduce yield by 0.50% times the reduction in Amar.
The values of basic variables, however, cannot be unilaterally adjusted, since they are completely determined by the values of the nonbasic variables. Perhaps a more accurate way to say this is that modifying the value of a basic variable requires modifying one or more nonbasic variables, and how you do that (combined with the reduced costs of the nonbasic variables you change) will determine the impact on the objective value.
The ranges tell you how much you can tweak any one objective coefficient while preserving optimality of the current basis. If you move an objective coefficient outside its range, a different corner of the feasible region may become optimal.