An Interval Efficiency Measurement in DEA When considering Undesirable Outputs

Renbian Mo,Hongyun Huang,Liyang Yang,Carlos Aguilar-Ibanez

doi:10.1155/2020/7161628

Renbian Mo, Hongyun Huang + Show 2 more

Open Access

https://doi.org/10.1155/2020/7161628

Copy DOI

Abstract

Data envelopment analysis (DEA) is a popular mathematical tool for analyzing the relative efficiency of homogenous decision-making units (DMUs). However, the existing DEA models cannot tackle the newly confronted applications with imprecise and negative data as well as undesirable outputs simultaneously. Thus, we introduce undesirable outputs into modified slack-based measure (MSBM) model and propose an interval-modified slack-based measure (IMSBM) model, which extends the application of interval DEA (IDEA) in fields that concern with less undesirable outputs. The novelties of the model are that it considers the undesirable outputs while dealing with imprecise and negative data, and it is slack-based. Furthermore, the model with undesirable outputs is proven translation-invariant and unit-invariant. Moreover, a numerical example is provided to illustrate the changes of the lower and upper bounds of the efficiency score after considering the undesirable outputs. The empirical results show that, without considering undesirable outputs, most of the lower bounds of the efficiency scores will be overestimated when the DMUs are weakly efficient and inefficient. The upper bound will also change after considering undesirable outputs when the DMU is inefficient. Finally, an improved degree of preference approach is introduced to rank the DMUs.

Highlights

Data envelopment analysis (DEA) is a popular mathematical tool for analyzing the relative efficiency of homogenous decision-making units (DMUs)
Is study develops the interval-modified slack-based measure (IMSBM) model to address undesirable outputs, which extends the application of interval DEA (IDEA) in fields that concern with less undesirable outputs, such as air pollutants, hazardous wastes, and nonperforming loans
Conclusion and Discussion is study develops the IMSBM model to address undesirable outputs, which extends the application of IDEA in fields that concern with less undesirable outputs, such as air pollutants, hazardous waste, and nonperforming loan

Summary

Introduction

Data envelopment analysis (DEA) is a popular mathematical tool for analyzing the relative efficiency of homogenous decision-making units (DMUs). Tone [21] proposed a slack-based measure SBM (a) of efficiency that puts aside assumptions about proportionate changes in inputs and outputs and deals directly with the input excesses and the output shortfalls of DMUs. Lotfi et al [22] integrated the SBM (a) model into IDEA to address interval data from the optimistic perspective and defined the upper and lower bounds of the SBM-efficiency scores, to classify DMUs into three subsets. Yang and Mo [26] considered these three characters simultaneously and extended the MSBM model to the interval MSBM (IMSBM) model, to evaluate the efficiency of particular DMUs with imprecise and negative data, and is slack-based. Our new IMSBM model is based on SBM (b), unlike the current IDEA models, and it considers undesirable outputs and both radial and nonradial efficiencies from the perspectives of slacks.

The MSBM and IMSBM Models with Undesirable Outputs

Application to Chinese City Commercial Banks