A novel Data Envelopment Analysis model for evaluating industrial production and environmental management system

Abstract

Industrial production and environmental management systems should be simultaneously considered for sustainable development. This paper evaluated the performance of an integrated two-stage system using a proposed type-2 fuzzy bi-objective two-stage slacks-based measurement Data Envelopment Analysis model with super efficiency. A Step Method was applied to solve for the Pareto optimal solution to ensure no implicit priority was given to one stage over the other, and a CV-based reduction method and generalized credibility based chance constrained programming were used to cope with the type-2 fuzzy variables. A case study in China was then developed from a time-perspective and a region-perspective, the results from which indicated that the overall performance of China's integrated system improved from 2005 to 2014, and the efficiency gap between the industrial production system and the environmental management system reduced, however, there was significant disparity shown across the different economic regions. Three comparative analyses were then conducted to highlight the superiority of the proposed model. The developed model was able to: measure efficiency scores and find proportionate ratios and disproportionate slacks for each DMU to decrease inputs for performance improvement, distinguish the DMU from DMUs with same efficiency value and indicate the maximum change scope for the inputs and outputs to maintain the DMU efficiency. In addition, type-2 fuzzy sets were incorporated to describe the fuzziness with greater flexibility, which can assist decision makers and produce more accurate, robust results.

Introduction

Remarkable changes have taken place in China since the reform and opening-up policy was implemented in 1978 with China now the second largest economy in the world with a GDP more than CNY10 trillion in 2015. Undoubtedly, industrial production has made the largest contribution to Chinese economic development, however, this rapid industrial development has resulted in serious environmental problems, which have hindered sustainable development. As a result, environmental management systems have become more important control and reduce the pollutants produced by industrial production systems. Therefore, to achieve sustainable development, it is necessary to evaluate combined industrial production and environmental management integrated systems to allow decision makers to identify inefficiencies in the integrated system and give specific insights for overall efficiency improvements.

Data Envelopment Analysis (DEA), first introduced by Charnes et al. (1978), has been widely used to obtain relative efficiency values for Decision Making Units (DMUs) to identify the possible sources of inefficiency in each DMU without the need to determine the weights for the multiple inputs in advance. As a better use of energy can lead to better environmental and economic performances (Khoshnevisan et al., 2015), attention has increasingly been focused on resource investment and environmental management efficiency analyses. For example, Wang et al. (2016b) utilized a DEA model to evaluate the energy and environmental performances from a provincial and regional perspective. Zhang et al. (2008) conducted an eco-efficiency analysis ofregional industry systems in China using DEA models, Chen and Jia (2017) completed an environmental efficiency analysis of China's regional industry using DEA models, Sueyoshi and Yuan (2015) considered air pollution in an economic development, and Li and Shi (2014) assessed the environmental protection’ efficiencies of different industrial sectors in China using an improved super-SBM DEA model.

However, previous research in this area has tended to only consider the undesirable outputs generated by industrial production systems that affect the environment and very few have assessed the environmental management and industrial production systems within an integrated framework. Therefore, in this paper, a DEA model is developed to evaluate an integrated two-stage system made up of an industrial production system and an environmental management system.

In a two-stage system, because traditional DEA models are not suitable as they consider the initial inputs and final outputs (Shamshirband et al., 2015), therefore have been many attempts to extend the DEA model two-stage system evaluations. Kao and Hwang (2008) introduced a multiplicative decomposition approach that calculated the product of the two sub-processes efficiencies to evaluate the whole process efficiency, and Cook et al. (2010) presented an additive decomposition approach; however, these decomposition methods were unable to evaluate performances in each stage. Despotis et al. (2016) introduced a multi-objective programming approach to evaluate a DMU to examine performance overall and at the subsystem level, in which all different subsystems are treated equivalently. Unlike decomposition approaches, the efficiency scores in each stage were estimated first and then, the overall efficiency score was obtained. In this paper, to assess the efficiencies in both stages, bi-objective programming and a two-stage DEA model were used to simultaneously optimize the two objective functions allowing for a comprehensive evaluation of the industrial production system and the environmental management system to inform decision makers on overall efficiency improvements.

As overall efficiency cannot be directly obtained, it is calculated by generating the efficiencies in each subsystem using a weighted sum method. The core of the weighted sum method is correctly determining the weights in each stage, for which there have been many previous approaches, such as weights based on investment proportions (Cook et al., 2010, Chen et al., 2009). However, weights for each stage can be based on different selected inputs. Allowing the same weight in each stage seems feasible (Maghbouli et al., 2014); however, this could distort (overestimate or underestimate) the real overall efficiency. Therefore, to represent a real, undistorted overall efficiency value, in this paper, a unique set of weights is determined based on the efficiency contribution to the integrated two-stage system in each stage.

Undesirable outputs are inevitably generated along with desirable outputs in an industrial production system. There have been three methods for modeling undesirable outputs. Seiford and Zhu (2002) multiplied each undesirable output by “-1” and then determined the proper translation vector w to make the negative undesirable output into a positive, Liu and Sharp (1999) treated undesirable outputs as inputs to solve a DEA model, in which the inputs and undesirable outputs had different proportional increases or decreases (Wang et al., 2016a), and Pathomsiri et al. (2008) applied a non-parametric directional output distance function to translate the undesirable variables with the direction varying depending on different decision makers. Efficiency can only be achieved when the desirable outputs are increasing and the undesirable outputs are reducing at the same time; therefore, in this paper, the undesirable outputs are treated as inputs in the integrated system to minimize inputs and undesirable outputs. As inputs and undesirable outputs may not change proportionately, the non-radical SBM DEA model first proposed by Tone (2001) is modified to find the DMU ratios and slacks so as to decrease the inputs or increase the outputs to ensure performance improvements. Some applications based on SBM models can be found in Bian et al. (2015) and Li and Shi (2014).

DMUs, however, may be simultaneously located at the production frontier, increasing evaluation difficulty and making it more difficult to identify improvements. Andersen and Petersen (1993) proposed a super efficiency DEA model to solve this problem, in addition to distinguishing a DMU from other DMUs with the same efficiency values, the super efficiency value can also indicate the scope for maximum change under a DMU maintenance premise (Yang et al., 2015). Therefore, in this paper, super efficiency is incorporated into the developed model to enhance its discrimination.

In addition, as observed values in realistic processes are often imprecise and vague, fuzzy sets based on numeric membership functions have been used in past researches (Kao and Liu, 2000, Puri and Yadav, 2014). For non-numeric membership functions, however, type-2 fuzzy sets are more suitable as these are able to describe fuzziness with a greater degree of flexibility than type-1 fuzzy sets (Abdullah and Zulkifli, 2015). As type-2 fuzzy sets have proven to be difficult to deal with directly, many reduction methods have been proposed. Three novel reduction methods for type-2 fuzzy variables were proposed by Qin et al. (2011), one of which was called the Critical Value (CV) based reduction method (Kundu et al., 2014, Zhou et al., 2016). In this paper, as industrial jobholders are constantly changing and utilization value of waste material has no unified standard faced with different decision makers, therefore, type-2 fuzzy sets are used to describe these variables.

This paper evaluates the performance of integrated two-stage industrial production and environmental management systems using a proposed type-2 fuzzy bi-objective two-stage SBM-DEA model with super efficiency. In this model, the intermediate variables attached to both stages need to be considered; for example, pollutants are undesirable outputs for the industrial production system, but are inputs for the environmental management system; bi-objective programming is adopted to evaluate the performance in the both stages within the whole framework so as to provide decision makers with specific and comprehensive information about overall efficiency improvements; auxiliary variables are added to find the proportionate ratios and disproportionate slacks for the DMU to decrease its inputs for performance improvement; super efficiency is incorporated to distinguish the DMU from DMUs with same efficiency values and to indicate the maximum change scope for promising DMU efficiency; and type-2 fuzzy data is used to describe the imprecise data. To solve the proposed model, a multi-objective optimization Step Method (STEM) is adopted to determine the Pareto optimal solution, and a CV-based reduction method and generalized credibility based chance constrained programming are used to cope with the type-2 fuzzy variables.

Above all, this paper differs from the existing related studies and makes the following main contributions to the current literature.

• Bi-objective programming is incorporated into a two-stage DEA model which includes both the industrial production and environmental management systems within a single framework so as to allow decision makers to have specific, comprehensive information when considering overall efficiency improvements.

• Proportionate and disproportionate reductions of inputs can be reflected by auxiliary variables while keeping a fixed output level.

• With super efficiency incorporated, the model is able to distinguish the DMU from DMUs with same efficiency value, and indicate the maximum change scope for the variables for the DMU to be efficient.

• Type-2 fuzzy sets are incorporated to describe the fuzziness with more flexibility, easing the burden of the decision maker, avoiding information losses or distortions, and producing more accurate, robust results.

• The Chinese integrated two-stage system is evaluated from both a time-perspective and a region-perspective, and some conclusions and managerial insights are represented.

The remainder of this paper is organized as follows. Section 2 gives the problem description and model development, and Section 3 introduces the solution procedure for the proposed model. In Section 4, a case study and several comparison analyses are given to demonstrate the feasibility and superiority of the developed model, and in Section 5, conclusions and recommendations are given.