Identifying the closest most productive scale size unit in data envelopment analysis

Finding the closest most productive scale size (MPSS) unit is an important issue in the data envelopment analysis (DEA) literature. The closest MPSS unit to the decision-making unit (DMU) under evaluation may be one of the existing (actually) observed MPSS units in the production technology. Also, finding the closest (actually) observed MPSS unit to the DMU under evaluation causes this DMU can easily achieve the optimal size for improving its performance because, in this case, the closest MPSS unit is only selected from the (actually) observed MPSS units. Hence, the manager (or decision-maker) of the DMU is more interested in considering the closest (actually) observed MPSS unit as a more accessible reference unit for his/her DMU than the closest non-observed MPSS unit. Hitherto several DEA-based models have been presented to determine the closest MPSS unit for the DMU under evaluation. However, the closest unit obtained from these models may not be MPSS, and also, this unit may not be one of the existing (actually) observed MPSS units in the technology. These problems indicate the drawbacks of these models. Hence, this research contributes to DEA by proposing three linear DEA-based models to tackle these drawbacks. Identifying the closest (actually) observed MPSS unit to the DMU under evaluation can be also used as a criterion for ranking the (actually) observed MPSS units as reference units for this DMU in the technology. This study also clarifies the managerial and economic implications of identifying the closest (observed) MPSS unit. Moreover, three numerical examples are given to illustrate the drawbacks of the previous models. Finally, a numerical illustration and an empirical application are provided to highlight the use of the proposed models.