Performance improvement on cross-efficiencies and applications to competitive advantages of Chinese cities

As a Data Envelopment Analysis (DEA) extension tool, cross-evaluation method was developed to evaluate Decision Making Units’ (DMUs) performances in a competitive situation with limited demand. It identifies DMUs with best performances and rank them by applying peer evaluation mode instead of self-evaluation mode. However, it has limitations in efficiency improvement. That is, it fails to give direct information on how to improve efficiencies of the inefficient DMUs. In this chapter, we propose an alternative way to apply cross-evaluation in efficiency improvement. First, an appropriate and feasible suggestion is proposed to minimize the variation between the weights of a DMU's own optimal Charnes-Cooper-Rhodes (CCR) efficiency and the weights guaranteeing its cross-efficiency score. We exploit several transformations to convert nonlinear programming into a linear one. As a result, an overall optimal set of the weights is obtained, which precisely illustrate the preferences of decision makers and exact characteristics of production process of the evaluated DMU. A further discussion is advanced to examine the existence of non-uniqueness of the weights and to differentiate various sets of the optimal weights by suggesting a unique feasible set of multipliers to best represent the alternative weights selection criterion. Moreover, we develop several models to reallocate the inputs and outputs of inefficient DMUs with minimum amelioration as well as consideration of the preference of decision makers. Finally, we apply our models to evaluate competitive advantages of Chinese cities.