Fuzzy data envelopment analysis in the presence of undesirable outputs with ideal points

Ali Ebrahimnejad,Naser Amani

doi:10.1007/s40747-020-00211-x

Abstract

Data envelopment analysis (DEA) is a prominent technique for evaluating relative efficiency of a set of entities called decision making units (DMUs) with homogeneous structures. In order to implement a comprehensive assessment, undesirable factors should be included in the efficiency analysis. The present study endeavors to propose a novel approach for solving DEA model in the presence of undesirable outputs in which all input/output data are represented by triangular fuzzy numbers. To this end, two virtual fuzzy DMUs called fuzzy ideal DMU (FIDMU) and fuzzy anti-ideal DMU (FADMU) are introduced into proposed fuzzy DEA framework. Then, a lexicographic approach is used to find the best and the worst fuzzy efficiencies of FIDMU and FADMU, respectively. Moreover, the resulting fuzzy efficiencies are used to measure the best and worst fuzzy relative efficiencies of DMUs to construct a fuzzy relative closeness index. To address the overall assessment, a new approach is proposed for ranking fuzzy relative closeness indexes based on which the DMUs are ranked. The developed framework greatly reduces the complexity of computation compared with commonly used existing methods in the literature. To validate the proposed methodology and proposed ranking method, a numerical example is illustrated and compared the results with an existing approach.

Highlights

Performance evaluation is a critically important procedure for the companies and organizations operating in the modern business world, where survival in the fiercely competitive business environment requires maintaining high levels of performance and efficiency
In "The proposed method", we present a methodology for solving the fuzzy DEA (FDEA) models with undesirable outputs based on the positive ideal point (PIP) and negative ideal point (NIP) formulations, and propose a fuzzy ranking algorithm for comparison and ranking of fuzzy efficiencies of decision making units (DMUs)
The main advantage of proposed method is that utilizing LP problems for solving FDEA models is highly economical compared with those derived from Puri and Yadav’s approach from a computational viewpoint, regarding the number of constraints and variables. These days a number of researchers have shown interest in the area of fuzzy data envelopment analysis and various attempts have been made to study the solution of fuzzy Data envelopment analysis (DEA) models

Summary

Introduction

Performance evaluation is a critically important procedure for the companies and organizations operating in the modern business world, where survival in the fiercely competitive business environment requires maintaining high levels of performance and efficiency. In the theoretical problems and especially those commonly solved by DEA models, inputs and outputs are usually expressed with exact values This is often inconsistent with the reality of business world, where, in many cases, our knowledge about the production process is inaccurate and the available data are imprecise or obscure. In "The proposed method", we present a methodology for solving the FDEA models with undesirable outputs based on the positive ideal point (PIP) and negative ideal point (NIP) formulations, and propose a fuzzy ranking algorithm for comparison and ranking of fuzzy efficiencies of DMUs. In "Numerical example", we solve a numerical example to demonstrate the performance of the proposed method.

Literature review

Concluding remarks

Compliance with ethical standards