Sensitivity analysis of the optimal assignment

This paper concentrates on sensitivity analysis of the optimal solution for the assignment problem (AP). Due to the high degeneracy of the AP, traditional sensitivity analysis, which determines the range in which the current optimal basis remains optimal, is impractical. Thus, changing the optimal basis does not ensure that the optimal assignment will be changed. Herein we investigate the properties of the AP and then propose several lemmas to determine two other types of sensitivity range. The first type is used to determine the range in which the current optimal assignment remains optimal. We further discuss what is the new optimal assignment when the changes surpass the range. The second type of sensitivity range is to determine those values of assignment model parameters for which the rate of change of optimal value function remains constant. An example is presented in order to demonstrate that the approaches are useful in practice.