Weak Disposability of Input and Output in a Nonparametric Production Analysis

In some production processes, unlike traditional data envelopment analysis (DEA), decision-making units (DMUs) consume widely used inputs since increasing them is more favorable for improving efficiency. Plastic wastes and rotten fruits are two instances of widely used inputs for recycling factories. In this paper, weak disposability of inputs will be presented with non-uniform profit factors for inputs, and then the model will be extended to cases that consume normal and widely used inputs, and produce desirable and undesirable outputs, simultaneously. Due to a nonlinear form of the final model, a linearization method is presented to provide a linear structure of the technology. A directional distance function approach, including weakly disposable inputs and outputs, is introduced to deal with widely used inputs and undesirable outputs. Finally, the approach will be tested by applying it to some domestic sewage treatment plants in China. Results show the proposed approach can discriminate between DMUs in a rational way and with less computational effort and also it can be used for the efficiency analysis when widely used inputs and undesirable outputs are presented.