Determining common weights in data envelopment analysis based on the satisfaction degree

Abstract

The traditional data envelopment analysis model allows the decision-making units (DMUs) to evaluate their maximum efficiency values using their most favourable weights. This kind of evaluation with total weight flexibility may prevent the DMUs from being fully ranked and make the evaluation results unacceptable to the DMUs. To solve these problems, first, we introduce the concept of satisfaction degree of a DMU in relation to a common set of weights. Then a common-weight evaluation approach, which contains a max–min model and two algorithms, is proposed based on the satisfaction degrees of the DMUs. The max–min model accompanied by our Algorithm 1 can generate for the DMUs a set of common weights that maximizes the least satisfaction degrees among the DMUs. Furthermore, our Algorithm 2 can ensure that the generated common set of weights is unique and that the final satisfaction degrees of the DMUs constitute a Pareto-optimal solution. All of these factors make the evaluation results more satisfied and acceptable by all the DMUs. Finally, results from the proposed approach are contrasted with those of some previous methods for two published examples: efficiency evaluation of 17 forest districts in Taiwan and R&D project selection.

Keywords:

• data envelopment analysis
• common weights
• satisfaction degree

Acknowledgements

The research is supported by National Natural Science Funds of China (No. 71501189, 71222106 and 71571173), Research Fund for the Doctoral Program of Higher Education of China (No.20133402110028), Foundation for the Author of National Excellent Doctoral Dissertation of P.R. China (No. 201279) and Top-Notch Young Talents Program of China.