存在非期望产出的决策单元阻塞问题研究

阻塞是指企业的过量投入引起生产效益下降的经济现象,近年来已经受到实业界与学术界的广泛关注。现有的决策单元阻塞问题研究普遍假设产出均是期望指标,然而,在实际生产中很多产出属于非期望指标。本文构建了同时存在期望产出和非期望产出决策单元的阻塞度量模型,该模型不仅可以判别决策单元是否存在阻塞,而且可以测算各项投入的阻塞程度,并给出了决策单元阻塞和技术无效之间的关系。最后,运用所提出的模型对我国上市商业银行的效率和阻塞情况进行了测算与分析,验证了本文模型的实用性与可行性。     

Data envelopment analysis: Prior to choosing a model

In this paper, we address several issues related to the use of data envelopment analysis (DEA). These issues include model orientation, input and output selection/definition, the use of mixed and raw data, and the number of inputs and outputs to use versus the number of decision making units (DMUs). We believe that within the DEA community, researchers, practitioners, and reviewers may have concerns and, in many cases, incorrect views about these issues. Some of the concerns stem from what is perceived as being the purpose of the DEA exercise. While the DEA frontier can rightly be viewed as a production frontier, it must be remembered that ultimately DEA is a method for performance evaluation and benchmarking against best-practice. DEA can be viewed as a tool for multiple-criteria evaluation problems where DMUs are alternatives and each DMU is represented by its performance in multiple criteria which are coined/classified as DEA inputs and outputs. The purpose of this paper is to offer some clarification and direction on these matters.     

Estimating two-stage network Slacks-based inefficiency: An application to Bangladesh banking

This paper studies the performance of nineteen private commercial banks and two government-owned banks in Bangladesh during the period 2005–2008 using a slacks-based inefficiency measure and the directional technology distance function. Performance is measured assuming a black-box production structure and then the black-box is opened and examined using a two stage network production structure. Current period performance in maximizing desirable loans and securities investments and minimizing bad loans depends on how efficiently inputs at one stage of production are transformed into intermediate outputs which are used at a subsequent stage of production. In addition, current period production of the intermediate output is constrained by the amount of non-performing loans that were generated in an earlier period.     

Measuring performance of two-stage network structures by DEA: A review and future perspective

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). An important area of development in recent years has been devoted to applications wherein DMUs represent two-stage or network processes. One particular subset of such processes is those in which all the outputs from the first stage are the only inputs to the second stage. The current paper reviews these models and establishes relations among various approaches. We show that all the existing approaches can be categorized as using either Stackelberg (leader-follower), or cooperative game concepts. Future perspectives and challenges are discussed.     

基于DEA的两阶段系统中间产品公平设定研究

在由两个子决策单元串联组成的两阶段系统中,公平设定中间产品目标对确保和激励两阶段相互合作以达到整个系统的最佳性能至关重要.数据包络分析(DEA)作为系统绩效评估的一种非参数方法吸引了众多学者的注意;基于此方法,本文提出一个考虑公平关切的两阶段DEA模型用于设定两阶段系统中间产品目标,并证明据此模型获得的设定方案正是一个纳什讨价还价博弈的均衡解.     

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.     

Integrated framework for robustness analysis using ratio-based efficiency model with application to evaluation of Polish airports

We consider a problem of evaluating efficiency of Decision Making Units (DMUs) based on their deterministic performance on multiple consumed inputs and multiple produced outputs. We apply a ratio-based efficiency measure, and account for the Decision Maker׳s preference information representable with linear constraints involving input/output weights. We analyze the set of all feasible weights to answer various robustness concerns by deriving: (1) extreme efficiency scores and (2) extreme efficiency ranks for each DMU, (3) possible and necessary efficiency preference relations for pairs of DMUs, (4) efficiency distribution, (5) efficiency rank acceptability indices, and (6) pairwise efficiency outranking indices. The proposed hybrid approach combines and extends previous results from Ratio-based Efficiency Analysis and the SMAA-D method. The practical managerial implications are derived from the complementary character of accounted perspectives on DMUs׳ efficiencies. We present an innovative open-source software implementing an integrated framework for robustness analysis using a ratio-based efficiency model on the diviz platform. The proposed approach is applied to a real-world problem of evaluating efficiency of Polish airports. We consider four inputs related to the capacities of a terminal, runways, and an apron, and to the airport׳s catchment area, and two outputs concerning passenger traffic and number of aircraft movements. We present how the results can be affected by integrating the weight constraints and eliminating outlier DMUs.     

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.     

DEA-based production planning

Production in large organizations with a centralized decision-making environment like supermarket chains or factories with many workshops, usually involves the participation of more than one individual unit, each contributing a part of the total production. This study is motivated by a production-planning problem regularly faced by the central decision-making unit to arrange new input and output plans for all individual units in the next production season when demand changes can be forecasted. Two planning ideas have been proposed in this paper. One is optimizing the average or overall production performance of the entire organization, measured by the CCR efficiency of the average input and output levels of all units. The other is simultaneously maximizing total outputs produced and minimizing total inputs consumed by all units. According to these two ideas, we develop two DEA-based production planning approaches to find the most preferred production plans. All these individual units, considered as decision-making units (DMUs), are supposed to be able to modify their input usages and output productions. A simple numerical example and a real world data set are used to illustrate these approaches.     

存在保证域的模糊非径向偏好DEA模型——基于中科院24个研究所的实证分析

数据包络分析（DEA）是一种非参数化的方法,用于评价具有类似输入和输出的决策单元的效率。传统的非径向DEA模型假设输入和输出数据均为准确值,且对权重变量不加以限制,本文构建了存在保证域的模糊非径向偏好DEA模型,并给出了一种基于模糊数截集的模型求解方法,有效地解决了输入和输出全部或部分为模糊数的决策单元评价问题。最后给出了一个中科院研究所效率评价的实例说明了方法的有效性。     

Benchmarking airports from a managerial perspective

Benchmarking airports is currently popular both in the academic literature and in practice but has proved rather problematic due to the heterogeneity inherent in any reasonably sized dataset. Most studies either treat the airport production technology as a black box, or separate the terminal and airside activities, assessing them individually. In this article we analyze airports as a single unit due to the direct complementarities, thus avoiding the artificial separation of inputs. Using data envelopment analysis (DEA), we open the black box in which a network describes the production process, thus demonstrating the sequential effects that separate final from intermediate outputs, including those under partial managerial control and those that are known to be non-discretionary. To further improve the benchmarking process, we identify appropriate peers for a case study of 43 European airports over 10 years, through a restricted reference mechanism according to pre-defined characteristics. Compared to basic DEA models, the results of the proposed structure provide more meaningful benchmarks with comparable peer units and target values that are potentially achievable in the medium term. By identifying each unit's individual reference set, unique outliers influence the performance measurement less severely than occurs under basic DEA. In addition, the formulations produce an implementation path that moves the airport towards the Pareto frontier gradually, taking into account the regulatory and business environment in which the unit is located.     

Ranking efficient units in DEA

Super-efficiency data envelopment analysis (DEA) model can be used in ranking the performance of efficient decision making units (DMUs). Because of the infeasibility problem associated with the super-efficiency DEA model, ranking has been restricted to the model where constant returns to scale and proportional changes in all inputs or all outputs are assumed. In fact, when super-efficiency is used as an efficiency stability measure, infeasibility means the highest super-efficiency. However, if super-efficiency is interpreted as input saving or output surplus achieved by a specific efficient DMU, infeasibility does not necessarily mean the highest super-efficiency. In order to obtain a complete ranking of efficient DMUs when the two assumptions are relaxed, a modified super-efficiency DEA model is proposed to overcome the infeasibility problem and to correctly capture the super-efficiency represented by the input saving or the output surplus. The current paper suggests using both input- and output-oriented super-efficiency models to characterize the super-efficiency when infeasibility occurs. As a result, we can rank the efficient DMUs if infeasibility occurs. The approach is applied to 20 largest Japanese companies and 15 US cities, respectively.     

DEA for non-homogenous parallel networks

In practice, systems are often composed of a group of sub-units. Each sub-unit has a set of performance metrics that are classified as inputs and outputs in data envelopment analysis (DEA). Conventional DEA views such a system as a “black-box”, other DEA-based models are developed to investigate the inner structure, either with a serial structure where components are connected by intermediate products, or with a parallel system under the key assumption that all sub-units are associated with the same type of inputs and outputs (in differing amounts) without the links. In many applications, however, this property of identical input/output factors may not hold. For example, factories may have various manufacturing lines whose inputs and outputs differ from one another. The current paper proposes a series of DEA models to accommodate settings where non-homogenous sub-units operate in parallel network structures with intermediate measures or links. Both the overall performance of the entire parallel network system and efficiency decomposition for each sub-unit can be evaluated through our method.     

Production efficiency in Indian agriculture: An assessment of the post green revolution years

In this paper we use the nonparametric method of Data Envelopment Analysis (DEA) to obtain Pareto-Koopmans measures of technical efficiency of individual states over the years 1970–71 through 2000–01 in a multi-output, multi-input model of agricultural production. We disaggregate overall efficiency into two distinct components representing output and input efficiencies and identify the contribution of individual outputs and inputs to the measured level of overall efficiency. Because introduction of modern inputs has been a major component of the process of modernization of Indian agriculture, we examine to what extent different states succeeded in utilizing the modern inputs compared to the traditional inputs. Variations in the DEA efficiency scores across states and over years is explained in terms of differences in various institutional and demographic factors in a second stage regression analysis.     

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.     

Measuring efficiency with products,by-products and parent-offspring relations: A conditional two-stage DEA model

In the usual data envelopment analysis (DEA) setting, as pioneered by Charnes et al. (1978) [1], it is assumed that a set of decision making units (DMUs) is to be evaluated in terms of their relative efficiencies in converting a bundle of inputs into a bundle of outputs. The usual assumption in DEA is that each output is impacted by each and every member of the input set. One particular area of recent research is that relating to partial input to output impacts where the main issue addressed is that in many settings not all inputs impact all outputs. In that situation the authors view the DMU as consisting of a set of mutually exclusive subunits, with each subunit having its own unique bundle of inputs and outputs. Examined as well in this area, is the presence of multiple processes for generating sets of outputs. Missing from that earlier work is consideration of the presence of outputs in the form of by-products, giving rise to a parent-offspring phenomenon. One of the modeling complications there is that the parent assumes two different roles; as an input affecting the offspring, while at the same time being the dominant output. This gives rise to a model that we refer to as conditional two-stage. Another complication is that in the presence of multiple processes, by-products often arise out of only a subset of those processes. In the current paper we develop a DEA-type of methodology to handle partial input to output impacts in the presence of by-products.     

Stage efficiency evaluation in a two-stage network data envelopment analysis model with weight priority

Conventional DEA models treat the entire production system as a black box and ignore its internal structures. To address this issue, many studies have examined the DEA efficiencies of two-stage systems in which all outputs of the first stage are the only inputs to the second stage. Based on game theory, the non-cooperative model and centralized model were developed for such a two-stage network structure. However, for the centralized model with multiple optimal solutions and the non-cooperative model, an assumption is required as to whether the first or second stage should be assigned the absolute priority for optimization. In many cases, certain circumstances might exist in which one stage does not completely dominate the other stage. In this paper, we develop a methodology for assessing the overall and stage efficiencies by considering the different and DMU-specific degree of priority given to the stages. Particularly, the non-cooperative model and the centralized model can be deemed as special cases. Moreover, we compare the proposed approaches with the existing approaches, which indicates that our approaches can greatly reduce the computational burden. Two empirical examples are used to demonstrate the proposed approach.     

Intra-Organizational and inter-organizational resource allocation in two-stage network systems

There are organizational systems, such as bank branches and two-stage supply chains, which are composed of multiple parallel two-stage structures. Resource allocation in these systems is to maximize the benefit of the overall organization from a global viewpoint. In this study, we consider two types of systems at an organizational level: a centralized organizational system treating the whole two-stage production process as a basic unit, and a decentralized organizational system including two sub-organizations (groups) treating one of the two-stage production processes as a basic unit. We propose intra-organizational and inter-organizational resource allocation plans for two different organizational systems, respectively. Specially, two modes of free intermediate resource allocation (Free IRA) and fixed intermediate resource allocation (Fixed IRA) are discussed for the decentralized organizational system. The proposed allocation plans are based on two-stage data envelopment analysis models with bi-level formulations, in which the upper-level model is to maximize the entire organizational effectiveness (total outputs minus total inputs) by determining the optimized input resources and output targets while the lower-level model is concerned with efficiency constraints of all decision-making units simultaneously. The developed methods are illustrated by an application to a real-world problem with 17 city bank branches.     

A Nerlovian cost inefficiency two-stage DEA model for modeling banks’ production process: Evidence from the Turkish banking system

By developing a two-stage model the paper examines the cost inefficiency levels of Turkish banks during the period from 2007 to 2016. Using the notion of Koopmans input efficiency we deconstruct the estimated Nerlovian cost inefficiency to the sum of slack-based allocative and technical inefficiency levels. Alongside the traditional inputs, intermediates and outputs used to model banks’ performance measure we additionally use their labor education quality factor as a non-discretionary input. This allows us to model how human capital factors affect a bank's revenue generation stage. Our findings suggest that cost inefficiency levels are driven mainly by a bank's ability to control its allocative inefficiency levels. The empirical evidence also shows that foreign banks perform better, suggesting that bank ownership structures matter when measuring cost performance. Finally, it is evident that the Global Financial Crisis (GFC) had a negative effect on banks’ ability to minimize their cost inefficiency levels. However, the post-crisis findings demonstrate that Turkish banks have started to recover from its negative effects, mainly by improving their allocative performance.     

DEA models for extended two-stage network structures

Liang et al. (2008) [1] developed DEA models based upon game approach to decompose efficiency for two-stage network structures where all outputs of the first stage are the only inputs to the second stage. This paper extends Liang et al. (2008) [1] by assuming that the inputs to the second stage include both the outputs from the first stage and additional inputs to the second stage. Two models are proposed to evaluate the performance of this type general two-stage network structures. One is a non-linear centralized model whose global optimal solutions can be estimated using a heuristic search procedure. The other is a non-cooperative model, in which one of the stages is regarded as the leader and the other is the follower. The newly developed models are applied to a case of regional R&D of China.