__What-if Analysis and the Sensitivity Report__

What-If analysis is predominantly relevant for models that do not capture all sources of uncertainty. Thus, if a particular model does not consider uncertainty, then what-if analysis can be used to observe the effect of changes in input values.

One simple way of doing what-if analysis is to change a value, and then resolve the problem to observe changes in the solution.

For example, let's suppose that it is possible to increase the supply capacity by ten units in any of the five suppliers in our transportation example. We want to determine where would we put these extra ten units?

One simple way of doing what-if analysis is to change a value, and then resolve the problem to observe changes in the solution.

For example, let's suppose that it is possible to increase the supply capacity by ten units in any of the five suppliers in our transportation example. We want to determine where would we put these extra ten units?

The above is a snapshot of the constraints table of the sensitivity report for our transportation problem. Here,

- Final value = total that is shipped from each supplier
- Right hand sides for the capacity constraints = supply limits
- Right hand sides for the demand constraints =quantities required by each customer
- Shadow prices = A shadow price is the change in the objective function for a unit of increase in the right hand side of the constraints. Since we're minimizing costs, a negative shadow price means savings.
- The last two columns tell us the operational range of the calculated shadow prices. For example, for supplier A, we can increase capacity by 20 units and save $4 per unit.

The above is a snapshot of the decision variables table of the sensitivity report for our transportation problem. Here, a reduced cost for each decision variable is calculated. This value is the amount by which the original cost needs to be reduced in order for the solution to include a shipment in that particular cell. For the cells that are already shipping products, the reduced cost is zero.

The sensitivity report provides very useful information for pricing decisions, value of resources and the robustness of the optimal solution.

The sensitivity report provides very useful information for pricing decisions, value of resources and the robustness of the optimal solution.