基于分段参数型DEA前沿面的投入—产出型技术效率

由传统DEA模型可以直接测算投入固定(产出固定)的条件下,面向产出(投入)的技术效率。尽管加型DEA模型同时考虑了投入和产出的松弛,但却不能像传统模型一样直接测算投入—产出型技术效率。为了直接由加性模型测算投入产出型技术效率,本文将利用DEA有效决策单元建立分段参数型DEA生产前沿面,并根据古典技术效率的定义,解决投入产出型技术效率的测算问题。研究发现,这种效率实质上是产出型技术效率与投入配置效率的乘积。由于同时考虑了投入和产出的技术无效性,与其它类型的技术效率相比,这种投入产出型技术效率的可分性更强。     

存在非期望输入输出的多阶段系统效率评价模型

现有多阶段DEA模型的研究普遍假设所有输入、输出均为期望指标, 对存在非期望指标的情况研究较少, 尚无对最初投入和中间产出带有非期望指标的研究。为此, 本文首先提出了输入、输出类型的判定方法, 并将其应用于存在非期望输入、输出的两阶段系统。进一步针对存在非期望指标的两阶段生产系统中同种输入、输出, 尤其中间产出类型判定一致与不一致的情况, 构建了相应的生产可能集以及两阶段DEA模型, 最后利用本文方法和模型对我国上市银行效率进行了评价。     

一种考虑整数约束的环境效率评价MOISBMSE模型

传统的基于数据包络分析的环境效率评价常常忽略投入、期望产出和非期望产出为离散型变量的可能性,从而无法精确处理现实中存在的具有整数特征的指标数据,一直以来影响着评价结果的精确性.本文以混合导向的整数DEA为基础,对超效率SBM模型进行拓展,构建了一种能够同时兼顾整数约束和非期望产出指标数据的超效率SBM模型,并在实例中采用搜索算法,对该模型进行求解并通过Bootstrap方法对结果进行修正.将每一个最优整数点与被评价决策单元之间的距离进行比较,可以找出最短距离所对应的最优整数点,即为其帕累托改进方向.该模型将为环境效率评价提供了适用范围更广泛的测度方法.     

一个新的考虑非期望产出的非径向-双目标DEA模型

如何实现对环境效率更准确的定量评价,是国际上从事DEA研究的学者们当前关注的问题之一。在传统DEA效率模型的基础上,综合考虑评价过程中期望产出与非期望产出之间的差异以及实际生产过程中人们追求期望产出最大化和非期望产出最小化的双重目标,构建非期望产出的非径向-双目标DEA环境效率评价模型,通过线性加权和法转化为一个求最大值的单目标线性规划问题。研究结果表明,这种新模型不仅可以分析DEA有效性与Pa-reto最优之间的关系,还利用决策单元的投影获得投入和产出的可调整量,从而提高考虑非期望产出的环境效率评价的精度。实证分析结果与现实情况的高度吻合,说明这种新的非径向-双目标DEA环境效率模型是有效的。     

基于未来效率的兼顾公平与效率的资源分配DEA模型研究——以各省碳排放额分配为例

根据需要实现的目标，评估各生产决策单元的投入产出效率及改进潜力，可以为资源分配提供重要参考。构建一个基于未来效率的兼顾公平与效率的资源分配DEA模型可以有效、灵活地解决该问题。该DEA模型首先根据历史数据计算每个生产决策单元过去各期的技术增长率，并预测各DMU未来的技术增长率，从而获得未来的生产前沿面。以此为基础，在九个硬性目标约束下，分三个步骤分别解决三个追求的软性目标：最大化期望总产出、最小化非期望总产出、最小化可变要素总投入。管理者不仅可以改变九个硬性目标的参数值，以及调整三个软性目标的优先顺序和软性目标参数值，进而形成各种兼顾效率与公平的资源分配方案。最后，运用该DEA模型评估了我国各省碳排放削减潜力，并形成了能够实现管理者期望目标的各省碳排放削减责任分配方案。     

评价相对效率的投入—产出型DEA

传统 DEA只能在固定投入或产出的条件下 ,从产出或投入角度测算决策单元相对效率 ,因而不能综合地反映决策单元的投入产出效果 .基于双目标规划 ,本文将提出从投入及产出角度评价决策单元相对效率的投入—产出型 DEA,并研究其相对有效性 .最后以沪市 1 6家高科技上市公司为应用实例 ,研究其相对经营效率     

评价相对效率的投入-产出型DEA

传统DEA只能在固定投入或产出的条件下,从产出或投入角度测算决策单元相对效率,因而不能综合地反映决策单元的投入产出效果.基于双目标规划,本文将提出从投入及产出角度评价决策单元相对效率的投入-产出型DEA,并研究其相对有效性.最后以沪市16家高科技上市公司为应用实例,研究其相对经营效率.     

随机环境下的多投入多产出生产前沿面估计

传统的DEA模型假设观测样本的投入产出都是确定型数据, 这使得DEA在实际应用中受到限制, 本文提出的基于拟似然估计的多投入多产出随机非参数包络数据 (PLE-StoNED) 方法拓展了这个假设, 能够估计随机环境下的生产前沿面.本文证明, 生产可能集假设条件下的前沿面可以用一个有凹凸性和单调性限制的函数来表示.相较之前的StoNED方法, 本文提出的方法可以估计随机环境下多投入多产出决策单元 (DMU) 的前沿面.通过Monte Carlo实验, 多投入多产出PLE-StoNED方法的有效性得到验证, 它可纠正DEA等传统方法产生的偏误.最后, 实证研究部分运用这一新提出的方法估计了中国大陆商业银行的生产前沿面和效率.本文提出的方法弥补了DEA缺乏统计性的不足, 可为决策者在随机环境下对多投入多产出决策单元进行生产力和效率评估提供决策参考.     

非期望产出、影子价格与无效决策单元的改进

本文首先建立考虑非期望产出的非参数DEA效率模型,从影子价格的视角论证DEA有效的充分必要条件,计算出无效DMU的可改进量,从而构建了一个考虑非期望产出、影子价格以及无效决策单元的改进的非参数DEA模型,然后通过一个算例进行实证分析,将这个新的模型和经典的SBM模型进行比较,结果显示两者的相关系数超过0.9,而且这一新模型还显示出一些SBM模型所没有的优良特性.这种新的非参数方法不仅能够对环境效率水平进行测度评价,而且相较于参数方法而言,它不需要事先设定规范的函数形式,对指标数据也不需要考虑计量单位问题,具有比较独特的优势.     

考虑满意度的两阶段DEA固定成本分摊方法

考虑具有相同的投入和产出的两阶段决策单元的固定成本分摊问题。将待分摊的固定成本作为一种新的投入，建立两阶段加性DEA模型。首先证明了各决策单元从自身角度出发可以找到至少一种分摊方案，使其自身整体和阶段效率都达到Pareto有效。然后证明了在公共的权重下，至少存在一种分摊方案可以使得各决策单元整体和阶段效率都达到Pareto有效。并给出了这样的有效成本分摊方案集。为了得到公平的成本分摊方案，定义了各DMU各阶段对分摊方案的满意度，最大化最小的满意度，可以得到最终的成本分摊方案。将问题拓展到两阶段存在共享投入的生产系统中，这些性质定理同样成立。数值算例部分将本文与Yu等（2016）的研究结果进行了对比，验证了本文方法的有效性，指出了本文方法的优越性。本文的方法综合考虑了效率和公平，得到的固定成本分摊方案公平合理。     

Slacks-based inefficiency approach for general networks with bad outputs: An application to the banking sector

In this paper the efficiency assessment of general networks of processes that produce both desirable and undesirable outputs is addressed. This problem arises in many contexts (e.g. transportation, energy generation, etc.). A general networks slacks-based inefficiency (GNSBI) measure can be computed using a simple linear program that takes into account the weak disposability of the bad outputs. The slacks-based inefficiency (SBI) of each process is also calculated. Target values for all inputs, outputs (both desirable and undesirable) and even intermediate products are also provided. The proposed approach is rather general and can accommodate many different network topologies and returns to scale assumptions. Two applications to the banking sector are presented: one to assess banks efficiencies and another to assess bank branches.     

Two-stage DEA models with undesirable input-intermediate-outputs

Data envelopment analysis (DEA) is a non-parametric approach for measuring the relative efficiencies of peer decision making units (DMUs). Many studies have examined DEA efficiencies of two-stage systems, where all the outputs from the first stage are the only inputs to the second stage. Although single-stage DEA models with undesirable input-outputs have been extensively studied, there still lacks of more systematical investigation on two-stage DEA with undesirable variables. For instance, depending on its operating model, even whether an intermediate variable is desirable or undesirable can be questionable for a particular two-stage system. Furthermore, most of the existing studies on two-stage systems focus on the case where only the final outputs are undesirable. In this work, we try to systematically examine two-stage DEA models with undesirable input-intermediate-outputs. Particularly, we utilize the free-disposal axioms to construct the production possibility sets (PPS) and the corresponding DEA models with undesirable variables. The proposed models are then used to illustrate some theoretical perspectives by using the data of China׳s listed banks.     

Eco-efficiency analysis of paper mills along the Huai River: An extended DEA approach

The objective of this paper is to estimate the ecological efficiency of paper mills along the Huai River in China. The main characteristic of the ecological efficiency evaluation problem is that an undesirable output of biochemical oxygen demand (BOD) and a non-discretionary input (BOD emission quota) should be considered simultaneously. By analyzing the impacts of the non-discretionary input on decision-making units’ (DMUs) desirable and undesirable outputs, a non-radial output-oriented DEA model is proposed. In the proposed model, we describe a new approach of defining reference set that requires reference units operate in a similar environment on average. We employ the model to provide efficient inputs/outputs targets for DMU managers to improve DMUs’ efficiencies. Based on the developed model, impacts of the non-discretionary input on DMUs’ returns are also analyzed. We illustrate the proposed model, using real data, for 32 paper mills along the Huai River in China.     

A slacks-based inefficiency measure for a two-stage system with bad outputs

We model the performance of DMUs (decision-making units) using a two-stage network model. In the first stage of production DMUs use inputs to produce an intermediate output that becomes an input to a second stage where final outputs are produced. Previous black box DEA models allowed for non-radial scaling of outputs and inputs and accounted for slacks in the constraints that define the technology. We extend these models and build a performance measure that accounts for a network structure of production. We use our method to estimate the performance of Japanese banks, which use labor, physical capital, and financial equity capital in a first stage to produce an intermediate output of deposits. In the second stage, those deposits become an input in the production of loans and securities investments. The network estimates reveal greater bank inefficiency than do the estimates that treat the bank production process as a black box with all production taking place in a single stage.     

Multi-valued measures in DEA in the presence of undesirable outputs

Data envelopment analysis (DEA) evaluates the relative efficiency of a set of comparable decision making units (DMUs) with multiple performance measures (inputs and outputs). Classical DEA models rely on the assumption that each DMU can improve its performance by increasing its current output level and decreasing its current input levels. However, undesirable outputs (like wastes and pollutants) may often be produced together with desirable outputs in final products which have to be minimized. On the other hands, in some real-world situations, we may encounter some specific performance measures with more than one value which are measured by various standards. In this study, we referee such measures as multi-valued measures which only one of their values should be selected. For instance, unemployment rate is a multi-valued measure in economic applications since there are several definitions or standards to measure it. As a result, selecting a suitable value for a multi-valued measure is a challenging issue and is crucial for successful application of DEA. The aim of this study is to accommodate multi-valued measures in the presence of undesirable outputs. In doing so, we formulate two individual and summative selecting directional distance models and develop a pair of multiplier- and envelopment-based selecting approaches. Finally, we elaborate applicability of the proposed method using a real data on 183 NUTS 2 regions in 23 selected EU-28 countries.     

The enhanced Russell-based directional distance measure with undesirable outputs: Numerical example considering CO2 emissions

Following the spirit of the enhanced Russell graph measure, this paper proposes an enhanced Russell-based directional distance measure (ERBDDM) model for dealing with desirable and undesirable outputs in data envelopment analysis (DEA) and allowing some inputs and outputs to be zero. The proposed method is analogous to the output oriented slacks-based measure (OSBM) and directional output distance function approach because it allows the expansion of desirable outputs and the contraction of undesirable outputs. The ERBDDM is superior to the OSBM model and traditional approach since it is not only able to identify all the inefficiency slacks just as the latter, but also avoids the misperception and misspecification of the former, which fails to identify null-jointness production of goods and bads. The paper also imposes a strong complementary slackness condition on the ERBDDM model to deal with the occurrence of multiple projections. Furthermore, we use the Penn Table data to help us explore our new approach in the context of environmental policy evaluations and guidance for performance improvements in 111 countries.     

A slack-based measure of efficiency in context-dependent data envelopment analysis

Data envelopment analysis (DEA) has been proven as an excellent data-oriented performance evaluation method when multiple inputs and outputs are present in a set of peer decision-making units (DMUs). In the DEA literature, a context-dependent DEA is developed to provide finer evaluation results by examining the efficiency of DMUs in specific performance levels based upon radial DEA efficiency scores. In DEA, non-zero input and output slacks are very likely to present after the radial efficiency score improvement. Often, these non-zero slack values represent a substantial amount of inefficiency. Therefore, in order to fully measure the inefficiency in DMU's performance, it is very important to also consider the inefficiency represented by the non-zero slacks in the context-dependent DEA. This study proposes a slack-based context-dependent DEA which allows a full evaluation of inefficiency in a DMUs performance. By using slack-based efficiency measure, we obtain different frontier levels and more appropriate performance benchmarks for inefficient DMUs.     

Efficiency evaluation of banks in China: A dynamic two-stage slacks-based measure approach

Operational processes of banks in China can be divided into productivity and profitability stages. Within this, non-performing loans can be treated as a carry-over variable, an undesirable output of the profitability stage in the previous period but an input to the profitability stage in the current period. Using this framework, this paper proposes a dynamic two-stage slacks-based measure model to evaluate the efficiencies of Chinese banks. Based on the proposed model, the measures of stage, period and period stage efficiencies are defined. The proposed approach is applied to evaluate the operational efficiency of banks in China during 2008–2012. Key findings are that banks in China show both technical and scale inefficiency during 2008–2012, which results from the inefficiencies of both the productivity stage and profitability stage; city-owned commercial banks are more overall technically efficient than state-owned commercial banks and joint-stock commercial banks although state-owned commercial banks show best practice for pure technical efficiency, and city-owned commercial banks perform better than joint-stock commercial banks for pure technical efficiency.