Sensitivity Analysis can be used to check the variation of the optimum solution when changing the coefficients of the objective function or constant values in constraints. Are there exist any other things to investigate using this approach?
Sensitivity analysis is useful to determine the robustness of the optimal solution. If the optimal solution changes significantly, when one of the problem parameters is changed only slightly, then the optimal solution is said to be sensitive to changes in that parameter, otherwise, it is robust.
Sensitivity analysis also gives insights into the problem under study. You can use it to validate your hypotheses about the problem or you can derive conclusions about the relationship of the optimal objective function value to the various parameters of the problem. This helps ground a problem from practice on a more reliable and intuitive basis, and demonstrates its applicability in practice.