A point-wise minimization model for data envelopment analysis considering environmental variables

Abstract

Environmental variables are widely recognized as a cause of differences in efficiency measurement. However, the existing literature on data envelopment analysis (DEA) in environmental factors ignores the impact of demand on output. To address this gap, we propose the Point-wise Minimization DEA model (PWMDEA), which considers contextual variables that affect demand and lead to differences in efficiency. The model obtains efficiency value by considering the minimum of virtual inputs and virtual demand. Then, efficiency is evaluated by minimizing the ratio of above minimum to virtual output. This one-step model avoids issues of multi-stage assumptions and requires less data, making it more applicable. Moreover, we demonstrate the accuracy of our new model by conducting simulations with given true efficiency values. The simulation results demonstrate that our model has the lowest ranking error when the output is affected by multiple inputs or when demand has a significant impact. In addition, we evaluate the efficiency of healthcare in 31 Chinese provinces by considering two environmental factors. The results suggest that provinces with lower financial investments or population loss received higher rankings from our proposed model. These findings provide plausible explanations and demonstrate the practical usefulness of our model.