An iterative method for determining weights in cross efficiency evaluation

- We prove that our approach produces a unique weight set for the cross efficiency evaluation.
- Our approach selects the weight set with the least zero weights among all weight sets of the DEA model.
- We do not impose any prior weight constraint.
- All the mathematical programs involved in our algorithm are linear programs, which can be easily solved.
- Our approach terminates within a finite number of iterations.

Cross efficiency evaluation in data envelopment analysis (DEA) is a commonly used skill for ranking decision making units (DMUs). However, the presence of multiple optimal weights in traditional DEA models leads to different cross efficiency scores for a DMU, which seriously affects the validity of this skill for ranking DMUs. Although many secondary-goal techniques have been proposed to address this issue, sometimes the weight sets determined by these techniques are still not unique. On the other hand, since zero weights make much information on inputs and outputs be ignored in cross efficiency evaluation, the number of them should be reduced as many as possible. The current approaches have not fully solved the above two problems. This paper proposes an iterative method for determining weights in cross efficiency evaluation, which not only ensures a unique weight set for positive input and output data but also reduces the number of zero weights maximally without imposing any prior weight restriction. Numerical examples are used to show the validity and superiorities of the proposed method in choosing a unique weight set and reducing the number of zero weights.