基于证据推理和前景理论的交叉效率排序方法研究

针对由交叉效率评价策略和交叉效率集结方法的多样性而造成评价结果不一致的问题,提出利用证据推理方法和前景理论,综合各个交叉效率评价策略的评价结果,实现对决策单元的统一评价。首先,分别将选用的交叉效率评价策略以及各个评价策略中的他评效率设置成一级指标和二级指标,依据算数平均和前景理论分别确定一、二级指标的权重;其次,依据他评效率确定二级指标置信度,利用证据推理方法将各个交叉效率评价策略的他评效率综合转换成决策单元被评价为有效的置信度。决策者可通过比较决策单元被识别为有效的置信度的大小来判断决策单元交叉效率的大小,进而实现对决策单元的排序;最后,通过案例验证和说明本文提出方法的有效性和实用性。     

DEA game cross-efficiency approach to Olympic rankings

A number of studies have used data envelopment analysis (DEA) to evaluate the performance of the countries in Olympic games. While competition exists among the countries in Olympic games/rankings, all these DEA studies do not model competition among peer decision making units (DMUs) or countries. These DEA studies find a set of weights/multipliers that keep the efficiency scores of all DMUs at or below unity. Although cross efficiency goes a further step by providing an efficiency measure in terms of the best multiplier bundle for the unit and all the other DMUs, it is not always unique. This paper presents a new and modified DEA game cross-efficiency model where each DMU is viewed as a competitor via non-cooperative game. For each competing DMU, a multiplier bundle is determined that optimizes the efficiency score for that DMU, with the additional constraint that the resulting score should be at or above that DMU 's estimated best performance. The problem, of course, arises that we will not know this best performance score for the DMU under evaluation until the best performances of all other DMUs are known. To combat this “chicken and egg” phenomenon, an iterative approach leading to the Nash equilibrium is presented. The current paper provides a modified variable returns to scale (VRS) model that yields non-negative cross-efficiency scores. The approach is applied to the last six Summer Olympic Games. Our results may indicate that our game cross-efficiency model implicitly incorporates the relative importance of gold, silver and bronze medals without the need for specifying the exact assurance regions.     

The use of OWA operator weights for cross-efficiency aggregation

Cross-efficiency evaluation is an effective way of ranking decision making units (DMUs) in data envelopment analysis (DEA). Existing approaches for cross-efficiency evaluation are mainly focused on the calculation of cross-efficiency matrix, but pay little attention to the aggregation of the efficiencies in the cross-efficiency matrix. The most widely used approach is to aggregate the efficiencies in each row or column in the cross-efficiency matrix with equal weights into an average cross-efficiency score for each DMU and view it as the overall performance measurement of the DMU. This paper focuses on the aggregation process of the efficiencies in the cross-efficiency matrix and proposes the use of ordered weighted averaging (OWA) operator weights for cross-efficiency aggregation. The use of OWA operator weights for cross-efficiency aggregation allows the decision maker (DM)’s optimism level towards the best relative efficiencies, characterized by an orness degree, to be taken into consideration in the final overall efficiency assessment and particularly in the selection of the best DMU.     

基于交叉效率和合作博弈的决策单元排序方法

在数据包络分析中，大量的交叉效率模型已被提出。然而选择不同的目标模型将实现不一样的交叉效率评价。本文基于针对单个决策单元实施的对抗型和仁慈型两个交叉效率模型，用合作博弈方法来研究交叉效率模型的选取，并利用Shapley值对决策单元进行排序。最后通过实例分析显示该排序方法充分利用了最小交叉效率和最大交叉效率的信息完全排序了所有决策单元，具有一定的综合性和合理性。     

Exploiting value system multiplicity and preference voting for robust ranking

Under a data envelopment analysis (DEA) framework, full ranking of a group of decision making units (DMUs) can be carried out through an adequate amalgamation of the cross-efficiency (CE henceforth) scores produced for each DMU. In this paper, we propose a ranking procedure that is based on amalgamating the weight profiles selected over the cross-evaluation rather than related CE scores. The new approach builds, for each DMU, a collective weight profile (CWP henceforth) by exploiting the preference voting system embedded within the matrix of weights, which views the assessing DMUs as voters and the input/output factors as candidates. The occurrence of zero votes is discussed as a special case and a two-level aggregation procedure is developed. The CWPs that are produced extend the concept of collective appreciation to the input/output factors of each DMU so that group dynamics is truly reflected, mainly in decision making circumstances where factor prioritization is necessary for making choices or allocating resources. The robustness of the proposed ranking approach is evaluated with three examples drawn from the literature.     

Konsensuale Effizenzbewertung und -verbesserung mittels DEA

This contribution is a new DEA approach in as much as it permits the decision making units (DMUs) to improve their respective efficiencies from the view of a peer rather than form their own self-appraisal attitudes. These authors study the output oriented model under constant scale efficiencies and first develop how a DMU can improve its performance by radial output increase or even by free output variation??in the light of the weight system of an arbitrary peer. The results are an improved cross-efficiency matrix and a maximum cross-efficiency matrix. Either of these matrices may serve as an appropriate instrument for a consensual choice of a peer??consensual among all DMUs. Input oriented models as well as simultaneous input/output considerations amend the so far developed results. A suitable example demonstrates all aspects of the new approach.     

中立型两阶段交叉效率评价方法

在数据包络分析中，已有的两阶段交叉效率评价方法，不仅只能用于基本两阶段网络结构，而且没有中立地分解子阶段效率。文章提出了一个既适用于基本两阶段网络结构，又适用于具有共享输入的两阶段网络结构的，中立型交叉效率评价方法。该方法定义自评时整体效率等于子阶段效率的加权和，在自评整体效率最大的前提下，从使各子阶段效率都尽可能大的角度为每个决策单元分别确定一组最优权重，进而通过互评计算决策单元整体和子阶段的最终效率得分。最后，通过两个实例验证了方法的实用、合理、有效。     

R&D project evaluation: An integrated DEA and balanced scorecard approach

We present and demonstrate a multi-criteria approach for evaluating R&D projects in different stages of their life cycle. Our approach integrates the balanced scorecard (BSC) and data envelopment analysis (DEA) and develops an extended DEA model. The input and output measures for the integrated DEA–BSC model are grouped in “cards” which are associated with a “BSC for R&D projects”. The BSC is embedded in the DEA model through a hierarchical structure of constraints that reflect the BSC balance considerations. We illustrate the proposed approach with a case study involving an industrial research laboratory that selects and executes dozens of R&D projects every year.     

Common benchmarking and ranking of units with DEA

This paper develops a common framework for benchmarking and ranking units with DEA. In many DEA applications, decision making units (DMUs) experience similar circumstances, so benchmarking analyses in those situations should identify common best practices in their management plans. We propose a DEA-based approach for the benchmarking to be used when there is no need (nor wish) to allow for individual circumstances of the DMUs. This approach identifies a common best practice frontier as the facet of the DEA efficient frontier spanned by the technically efficient DMUs in a common reference group. The common reference group is selected as that which provides the closest targets. A model is developed which allows us to deal not only with the setting of targets but also with the measurement of efficiency, because we can define efficiency scores of the DMUs by using the common set of weights (CSW) it provides. Since these weights are common to all the DMUs, the resulting efficiency scores can be used to derive a ranking of units. We discuss the existence of alternative optimal solutions for the CSW and find the range of possible rankings for each DMU which would result from considering all these alternate optima. These ranking ranges allow us to gain insight into the robustness of the rankings.     

一种新的基于双前沿面的交叉效率方法及其应用

本文将双前沿面效率评价的思想引入到传统交叉效率模型中，同时，针对双前沿面交叉效率方法中仁慈型和激进型交叉效率策略无法抉择，以及这两种交叉效率策略的应用范围有限的不足，提出了一种新的基于双前沿面的交叉效率方法。该方法的基本思想是选取一个理想决策单元和负理想决策单元，使用被评价决策单元的权重来计算理想决策单元和负理想决策单元的效率，并使被评价决策单元的效率尽可能接近理想解的效率，同时，尽可能远离负理想解的效率。根据该思想，分别在乐观前沿面和悲观前沿面下求解交叉效率值并进行集结，避免了由于前沿面的选择不同导致的差异以及决策者对仁慈型和激进型交叉效率策略进行抉择的困难。最后，将本文方法与现有方法进行对比分析，并将本文方法应用于我国东部地区10个省(直辖市)的创新效率评价中，以验证方法的有效性。     

DEA-based fixed cost allocation in two-stage systems: Leader-follower and satisfaction degree bargaining game approaches

This paper proposes new fixed cost allocation approaches for allocating a fixed cost among decision-making units (DMUs) with two-stage structures under the framework of data envelopment analysis (DEA). Firstly, we give the set of possible fixed cost allocations, prove that all DMUs can be overall efficient when evaluated by a common set of weights after fixed cost allocation. Secondly, from a centralized point of view, we consider the competition between the DMUs’ two stages in fixed cost allocation and regard these two kinds of stages as two unions. Then, we incorporate leader-follower models to propose a fixed cost allocation approach to handle the situation in which the two unions make decisions sequentially. Based on the result of these models, a concept of satisfaction degree of each union on a fixed cost allocation is presented. A satisfaction degree bargaining game model is then proposed to obtain a fixed cost allocation which is a bargaining equilibrium of the two unions. We show that the proposed approaches always obtain a fixed cost allocation that is proportionally invariant. Additionally, the satisfaction degree bargaining game approach automatically guarantees the uniqueness of the fixed cost allocation. These properties make the fixed cost allocation generated by our approaches more stable and more acceptable. Finally, a numerical example and an application of fixed cost allocation among bank branches are given to illustrate the proposed approach and to compare it with a benchmark approach among the current studies, respectively.     

决策单元交叉效率的自适应群评价方法

传统交叉效率评价方法因决策单元偏好权重不唯一而难以操作,因交叉效率有效性分值平均化集结而难以被接受。目前的学者通常围绕决策单元指标权重的确定性分配方法、交叉效率有效性分值的去平均化集结等分别开展研究。本文将交叉效率评价方法中自评互评相结合的评价模式看作群决策过程,即每个决策单元既是一个被评对象,又是一个决策"专家",提出了一种决策单元交叉效率的自适应群评价方法,将决策单元偏好权重的确定和交叉效率有效性分值的去平均化集结作为同一个决策过程,根据每个决策单元的评价结果与群体评价结果的接近程度,同步迭代调整决策单元的"专家"权重和决策单元自评产生的、并提供给其他被评价决策单元的一组确定的偏好指标权重。实验验证与实例运用分析表明,该方法收敛效果良好,能得到客观稳定的决策单元交叉效率有效性分值及排序。     

A real option theoretic fuzzy evaluation model for enterprise resource planning investment

The high failure rate of ERP implementation is due to a common pitfall that ERP projects are often enacted as merely investment into installation of IT infrastructure, rather than systematic planning of operation changes, business process re-engineering and a paradigm shift for the operation and management. To manage ERP investment in a changing environment for high payoff, this paper adopts a real option theoretic method. Fuzzy payoff valuation is introduced to deal with uncertainties in order to minimize the risk of failure. The proposed ERP evaluation model is geared towards small and medium enterprises. A case study is presented to validate the proposed fuzzy real options. The results indicate the potential of modeling ERP investment as “Expand”, “Contain” and “Abandon” options in different scenarios. The fuzzy real option model bestows a novel ex-ante cost analysis for justifying ERP investment in the implementation cycle.     

Allocating a fixed cost based on data envelopment analysis and satisfaction degree

This paper uses the Data Envelopment Analysis (DEA) technique to solve the problem of allocating a fixed cost across a set of comparable decision making units (DMUs) in a fair way. It first investigates the effect of the fixed cost on each DMU and on the collection of DMUs. Next we prove that there exist some cost allocations which can make each DMU and the collection of DMUs efficient. We show that such a cost allocation is unique and equivalent to the proportional sharing method if the fixed cost allocation problem is a one-dimensional case. In a multidimensional case, the fixed cost allocations may not be unique. This paper defines the concept of satisfaction degree, and proposes a maxmin model and a corresponding algorithm to generate a unique fixed cost allocation. Finally, the proposed approach has been applied to a data set from prior literature.     

Towards a global economy

The author, a well known consultant on planning for technology, argues cogently for planning on a global scale. The alternative to widespread recognition and acceptance of the need for global planning is, he says: “the choice of which of the weapons existing we, as a species, shall use to commit suigenicide.”     

基于可变权重的DEA效率评价模型

传统DEA模型将投入、产出权重视为固定变量。为了更合理地对决策单元的效率进行评价,本文研究了如何将有关投入、产出变量的权重的更多信息融入效率评价模型,提出了可变权重的概念,给出了一种基于可变权重的DEA效率评价模型。本文模型是CCR模型的推广。在有关权重信息可得的前提下,本文模型较之CCR模型中效率评价上更为合理。但是,如何准确度量投入、产出权重并将其函数化,是本文方法应用的难点。一个算例分析演示了本文模型。     

Efficiency evaluations with context-dependent and measure-specific data envelopment approaches: An application in a World Bank supported project

We evaluate the efficiency of decision making units (DMUs) in a World Bank supported Social Risk Mitigation Project (SRMP) in Turkey through context-dependent and measure-specific data envelopment analysis (DEA) approaches. The results suggest that the efficiency evaluations with context-dependent and measure-specific DEA play various roles in an organization such as setting attainable targets to DMUs, setting long and short term targets to DMUs separately, grouping of DMUs, and improving internal competition between DMUs. Four main contributions of this study can be summarized as follows. Firstly, the study shows the applicability of context-dependent and measure-specific DEA methodologies in a World Bank supported large scale project to increase the effectiveness of the project. Secondly, it outlines some important managerial conclusions of context-dependent DEA clustering approach. Moreover, we propose an alternative approach for attractiveness scores computations in case of exogenous group formations. Finally, the study proposes and applies measure-specific version of context-dependent DEA approach.     

Decision making in the newsvendor problem: A cross-national laboratory study

In this paper, we conduct a laboratory experiment using the classic newsvendor problem to examine cross-national differences in inventory ordering patterns between Chinese and American decision makers based on a theoretical examination of the role of the Doctrine of the Mean in Chinese decision making. Drawing on the theory of context-dependent preferences (specifically extremeness aversion), we also revisit the flat-maximum hypothesis of Bolton and Katok [12], i.e., “thinning the set of order options leads to newsvendor decisions that achieve a higher proportion of maximum expected profit.” The results show that the “pull-to-center” effect is more prominent for Chinese than Americans, i.e., average order quantities of Chinese subjects are closer to the anchor of mean demand than those of American subjects. Furthermore, we find that thinning the set of order options such that the optimal order quantity is a middle option, not an extreme option in the choice set, leads to better performance in newsvendor decisions, which complements the flat-maximum hypothesis.     

A technical note on “A fuzzy set approach for R&D portfolio selection using a real options valuation model” by Wang and Hwang (2007)

In this paper, three critical issues with the paper “A fuzzy set approach for R&D portfolio selection using a real options valuation model”, coauthored by Wang and Hwang and published in Omega 2007 are addressed. Shortcomings of the original work are highlighted and corrective measures to improve the approach are proposed.     

基于理想决策单元参照求解策略的DEA交叉效率评价模型

在已有关于DEA交叉效率评价模型中,激进型模型和仁慈型模型会因评价结果不一致而导致实际应用中难以对它们予以抉择的难题;中立型模型虽在形式上规避了前述问题,但其本身存在着理论偏差。针对上述问题,基于TOPSIS的理想点构造方法,提出了一种关于DEA交叉效率评价的新模型,即基于理想决策单元参照求解策略的DEA交叉效率评价模型。该模型不仅具有理论的严谨性,可以规避激进型模型与仁慈型模型之间的选择难题,而且相对于它们而言能够更好地坚持DEA最有利于被评价决策单元的基本思想。数值模拟分析表明新模型具有解决实际问题的较好适用性。