Data Envelopment Analysis With Common Weights: The Compromise Solution Approach

Chiang Kao and Hsi-Tai Hung

Department of Industrial and Information Management

National Cheng Kung University

Tainan, Taiwan, ROC

E-mail: [email protected]

Abstract

A characteristic of Data Envelopment Analysis (DEA) is to allow individual decision making units (DMUs) to select the factor weights which are most advantageous for them in calculating their efficiency scores. This flexibility in selecting the weights, on the other hand, deters the comparison among DMUs on a common base. In order to rank all the DMUs in the same scale, this paper proposes a compromise solution approach for generating common weights under the DEA framework. The efficiency scores calculated from the standard DEA model are regarded as the ideal solution for the DMUs to achieve. A common set of weights which produces the vector of efficiency scores for the DMUs closest to the ideal solution is sought. Based on the generalized measure of distance, a family of efficiency scores called “compromise solutions” can be derived. The compromise solution has several attractive properties not enjoyed by the solutions derived from the existing methods of common weights. An example of forest management illustrates that the compromise solution approach is able to generate a common set of weights which not only differentiates efficient DMUs but also detects abnormal efficiency scores on a common base.