Estimating Returns to Scale in the Presence of Undesirable Factors in Data Envelopment Analysis

This research identifies returns to scale (RTS) of efficient decision making units (DMUs) with desirable (good) and undesirable (bad) inputs and outputs by presenting a new DEA (data envelopment analysis) approach. In this study, we first introduce a new input-output oriented model to determine efficient DMUs in the presence of undesirable factors and then, returns to scale of these DMUs are estimated by presenting a new non-radial DEA model. So far several RTS approaches has been proposed in DEA literature by many researchers, such as Banker and Thrall’s, Golany and Yu’s, Khodabakhshi’s et al., and Eslami and Khoveyni’s RTS approaches. In the proposed approaches, all inputs and outputs are respectively considered as desirable inputs and outputs while in real world, both desirable and undesirable data may be present. Note that advantage of our proposed approach is capable of estimating RTS of efficient DMUs in the presence of desirable and undesirable data. It is noticeable that, since an inefficient decision making unit (DMU) has more than one projection on the empirical function thus different returns to scales can be obtained for projections of the inefficient DMU by using our proposed RTS approach. Lastly, an empirical example for illustrating purpose is presented and also directions for future research are suggested.