Qingxian An

Total-factor energy efficiency evaluation of Chinese industry by using two-stage DEA model with shared inputs

Chinese industry has developed greatly since China implemented its “reform and opening-up” policy in 1978. With the rapid development of industry, the problems of growing energy consumption and environmental pollution are drawing increasing attention from government managers and scholars. This paper divides industrial systems into two stages, an energy utilization stage and a pollution treatment stage, for accurately evaluating the total-factor energy efficiency as well as the overall efficiency. We build a new two-stage data envelopment analysis model with shared inputs to open the “black box” of efficiency measurement in traditional energy efficiency methods. Applying the model to data for Chinese regions, we can display the advantages and disadvantages of these two stages of industry. The results show that (1) the performance of Chinese industry improved during the years 2006–2010; (2) the energy utilization stage performance was better than that of the pollution treatment stage, but the gaps reduced year by year; and (3) energy efficiency increased during this period. Based on these results, some policy recommendations are given.

Measuring slacks-based efficiency for commercial banks in China by using a two-stage DEA model with undesirable output

Bank industry plays a critical role in the economic development of China. In this paper, we develop a new two-stage data envelopment analysis approach for measuring the slacks-based efficiency of Chinese commercial banks during years 2008–2012, where the banking operation process of each bank is divided into a deposit-generation stage (division) and a deposit-utilization stage (division). In the approach, the increase of desirable outputs and the decrease of undesirable outputs are simultaneously considered in order to identify the inefficiency of a bank. Three efficiency statuses are first defined for such a system to investigate its input-output performance and divisional performances, and a full efficiency status is then defined based on these statuses. The empirical results show that the improvement of the banks’ performances during this period was mainly contributed by the improvement of deposit-utilization stage. Besides, the results also show that our approach can provide a benchmark for the intermediate measures of the two stages of an inefficient bank.

An Approach for Group Decision Making With Interval Fuzzy Preference Relations Based on Additive Consistency and Consensus Analysis

Interval fuzzy preference relations (IFPRs) that can simply denote the lower and upper bounds of decision makers’ uncertain judgments are keenly studied by researchers and are widely used in practical decision-making problems. Consistency analysis is vitally important to avoid illogical ranking orders. First, this paper analyzes issues in previous additive consistency concepts for IFPRs. Then, it presents a new additive consistency definition that overcomes issues in previous ones. A linear programming model to judge the additive consistency of IFPRs is constructed, and a method to derive additive consistent IFPRs is proposed. Furthermore, a goal programming model to determine missing values in an incomplete IFPR is built, which have the highest consistent level with respect to known values. Regarding group decision making, a group consensus index is defined to measure the consensus of individual IFPRs, and an approach to improve the consensus level is introduced. Finally, a method for group decision making with IFPRs is developed, which can address incomplete and inconsistent cases. Associated examples are given to show the efficiency and feasibility of the developed theoretical results and comparative analysis is made.

A consistency and consensus-based method to group decision making with interval linguistic preference relations

Preference relations are a powerful tool to address decision-making problems. In some situations, because of the complexity of decision-making problems and the inherent uncertainty, the decision makers cannot express their preferences by using numerical values. Interval linguistic preference relations, which are more reliable and informative for the decision-makers’ preferences, are a good choice to cope with this issue. Just as with the other types of preference relations, the consistency and consensus analysis is very importance to ensure the reasonable ranking order by using interval linguistic preference relations. Considering this situation, this paper introduces a consistency concept for interval linguistic preference relations. To measure the consistency of interval linguistic preference relations, a consistency measure is defined. Then, a consistency-based programming model is built, by which the consistent linguistic preference relations with respect to each object can be obtained. To cope with the inconsistency case, two models for deriving the adjusted consistent linguistic preference relations are constructed. Then, a consistency-based programming model to estimate the missing values is built. After that, we present a group consensus index and present some of its desirable properties. Furthermore, a group consensus-based model to determine the weights of the decision makers with respect to each object is established. Finally, an approach to group decision making with interval linguistic preference relations is developed, which is based on the consistency and consensus analysis. Meanwhile, the associated numerical examples are offered to illustrate the application of the procedure.

A DEA-based approach for allocation of emission reduction tasks

Rapid economic growth has led to increasing pollution emission, leading governments to require emission reductions by specific amounts. The allocation of specific emission reduction tasks has become a significant issue and has drawn the attention of academia. Data envelopment analysis (DEA) has been extended to construct the allocation of emission reduction tasks model. These previous DEA-based approaches have strong assumptions about individual enterprise production. In this paper, we propose a new method to accurately assess the production, using each enterprise’s previously observed production to construct its own production technology plan. With emission permits decreased, the enterprise can have new production strategy based on its own technology. Assuming emission permits can be freely bought and sold, we show how each enterprise can determine the optimal amount of emission allowance that should be used for production, which may leave some allowance to be sold for extra profit or may require the purchase of permits from other firms. Considering the limitation on the total allowance from emission permits, we introduce the concept of satisfaction degree and use it in maximising the minimum enterprise satisfaction degree. Last, a numerical example is presented and an empirical application is given to verify the proposed approach.

A new approach for fair efficiency decomposition in two-stage structure system

Traditional data envelopment analysis has been applied to many areas to evaluate the relative efficiency of decision making units and it takes the internal structure of system as a “black box”. Recently, many two-stage DEA models are built to open up the “black box” of a two-stage system, where the outputs of the first stage are taken as the inputs for the second stage. By applying the two-stage DEA, more inefficiency in the system can be measured. The overall efficiency and divisional efficiencies of DMUs can be simultaneously obtained. Although some works take measures to decompose the overall efficiency into two divisional efficiencies, few works consider the competition between two stages because one stage has larger efficiency value and the other one will have smaller value. More importantly, in previous decomposition works, there are few works considering a DMU’s individual performance among its homogenous divisions. Based on the difference between two divisional performance (reference ratio), in this paper, a new model with fairness is proposed to decompose the overall efficiency and further applied to measure Chinese commercial banks’ performance from both the individual and overall perspectives.

Interval cross efficiency for fully ranking decision making units using DEA/AHP approach

Data envelopment analysis (DEA) is a popular technique for measuring the relative efficiency of a set of decision making units (DMUs). Fully ranking DMUs is a traditional and important topic in DEA. In various types of ranking methods, cross efficiency method receives much attention from researchers because it evaluates DMUs by using self and peer evaluation. However, cross efficiency score is usual nonuniqueness. This paper combines the DEA and analytic hierarchy process (AHP) to fully rank the DMUs that considers all possible cross efficiencies of a DMU with respect to all the other DMUs. We firstly measure the interval cross efficiency of each DMU. Based on the interval cross efficiency, relative efficiency pairwise comparison between each pair of DMUs is used to construct interval multiplicative preference relations (IMPRs). To obtain the consistency ranking order, a method to derive consistent IMPRs is developed. After that, the full ranking order of DMUs from completely consistent IMPRs is derived. It is worth noting that our DEA/AHP approach not only avoids overestimation of DMUs’ efficiency by only self-evaluation, but also eliminates the subjectivity of pairwise comparison between DMUs in AHP. Finally, a real example is offered to illustrate the feasibility and practicality of the proposed procedure.

Resource allocation of a parallel system with interaction consideration using a DEA approach: an application to Chinese input–output table

ABSTRACT Resource allocation is a popular and important issue in the enterprise management. Recently, data envelopment analysis (DEA) as a non-parametric method for measuring the performance of decision-making units (DMUs) has brought a new flavour to this issue. However, most of resource allocation works by DEA focused on single stage system or consider the internal production process of the system as a ‘black box.’ With the competition and relation among economic entities enhance, the system becomes more and more complex and interactive. To go inside the ‘black box’, in this paper, we propose a new DEA approach to allocate the resource in a bidirectional interactive parallel system. We consider not only the resource allocation of a certain DMU, but also the resource allocation of all DMUs for a centralized decision maker through centralized models. Moreover, the leader–follower relationship between two subunits is studied by a non-cooperative model as a theoretical extension. Finally, the approach is applied to Chinese input–output table in the cooperation scenario. We compare our approach with the traditional approach and find that it can obtain more potential gains.

A Natural Method for Ranking Objects from Hesitant Fuzzy Preference Relations

Hesitant fuzzy preference relations (HFPRs) are efficient tools to denoting the decision maker’s judgements that permit the decision makers to compare objects using several values in [0, 1], and the number of elements in different hesitant fuzzy elements may be different. After reviewing the previous researches about decision making with HFPRs, one can find that there are several limitations. To avoid these issues and to guarantee the reasonable ranking order, this paper introduces a new additive consistency concept for HFPRs. Different from the previous consistency concepts, the new concept neither needs to add values into hesitant fuzzy elements nor disregards any information offered by the decision makers. To measure the additive consistency of HFPRs, two 0-1 mixed programming models are constructed. Meanwhile, an additive consistency based 0-1 mixed programming model is established to determining the missing values in incomplete HFPRs that can address the situation where ignored objects exist. Then, an algorithm to obtaining the hesitant fuzzy priority weight vector from (incomplete) HFPRs is provided. Considering group decision making, a new group consensus index is defined, and an interactive approach to improving the group consensus level of individual HFPRs is offered. Furthermore, a probability distance measure between two HFPRs is defined to deriving the weights of the decision makers. According to the additive consistency and consensus analysis, an approach to group decision making with incomplete and inconsistent HFPRs is performed. Finally, two practical numerical examples are provided, and comparison analysis is offered.

Ranking ranges, performance maverick and diversity for decision-making units with interval cross-efficiency matrix

ABSTRACTAn alternative strategy in cross-efficiency evaluation is to take into consideration all the possible choices of data envelopment analysis weights that all decision-making units (DMUs) can ...