An Interval Efficiency Measurement without Sign Restrictions in Data

Mostly, all conventional DEA models assume that input-output data are precise and nonnegative, but in real-life application, this condition is mostly not applicable. Through progressive development in the methodology of DEA, some models separately deal with imprecise and negative data. In this study, the IMSBM model is proposed to evaluate the performance of a set of homogenous DMUs with imprecise and negative input-output data. The IMSBM model is far superior to models with similar capability because it considers the inefficiency caused by both radial and nonradial slacks. The lower and upper bounds of interval efficiency calculated by the IMSBM model reflect the performance of observed DMU in most unfavourable and most favourable situations. Further, it is proved that the IMSBM model is units invariant, monotone, and translation invariant. Moreover, we elaborate both bounds of the interval efficiency are in the range of [0,1]. The degree of preference approach is introduced to rank the DMUs. In addition, we compare the interval efficiency scores calculated by the IMSBM model and the interval SORM model and explain the reason for the difference between the scores. By adjusting the weights of inputs and outputs, it is found that only inefficiency scores fluctuate with slack weights.