A semi-oriented radial measure for measuring the efficiency of decision making units with negative data,using DEA

Data Envelopment Analysis (DEA) is a nonparametric method for measuring the efficiency of a set of decision making units such as firms or public sector agencies, first introduced into the operational research and management science literature by Charnes, Cooper, and Rhodes (CCR) [Charnes, A., Cooper, W.W., Rhodes, E., 1978. Measuring the efficiency of decision making units. European Journal of Operational Research 2, 429–444]. The original DEA models were applicable only to technologies characterized by positive inputs/outputs. In subsequent literature there have been various approaches to enable DEA to deal with negative data.     

A game theoretical model of DEA efficiency

Motivated by the inherent competitive nature of the DEA efficiency assessment process, some effort has been made to relate DEA models to game theory. Game theory is considered not only a more natural source of representing competitive situations, but also beneficial in revealing additional insights into practical efficiency analysis. Past studies are limited to connecting efficiency games to some particular versions of DEA models. The generalised DEA model considered in this study unifies various important DEA models and presents a basic formulation for the DEA family. By introducing a generalised convex cone constrained efficiency game model in assembling the generalised DEA model, a rigorous connection between game theory and the DEA family is established. We prove the existence of optimal strategies in the generalised efficiency game. We show the equivalence between game efficiency and DEA efficiency. We also provide convex programming models for determination of the optimal strategies of the proposed games, and show that the game efficiency unit corresponds to the non-dominated solution in its corresponding multi-objective programming problem. Our study largely extends the latest developments in this area. The significance of such an extension is for research and applications of both game theory and DEA.     

Value-based DEA models: application-driven developments

Data envelopment analysis (DEA) is an approach based on linear programming to assess the relative efficiency of peer decision-making units (DMUs). Typically, each DMU is free to choose the weights of the factors used in its evaluation. However, the evaluator's preferences may not warrant so much freedom. Several approaches have been proposed to allow the incorporation of managerial preferences in DEA, but few address the additive DEA model specifically. This paper presents additive DEA models that use multi-criteria decision analysis concepts to incorporate managerial preferences, and presents the corresponding preference elicitation protocols. The models developed allow the incorporation of preferences at different levels: on valuing performance improvements, on introducing weight restrictions, and on finding adequate targets. These were application-driven developments, resulting from discussing modelling options and preliminary results with the top-level management of a retail chain in the context of an assessment of stores’ performance, also described in this paper.     

Preface to topics in data envelopment analysis

This paper serves as an introduction to a series of three papers which are directed to different aspects of DEA (Data Envelopment Analysis) as follows: (1) uses and extensions of window analyses' to study DEA efficiency measures with an illustrative applications to maintenance activities for U.S. Air Force fighter wings, (2) a comparison of DEA and regression approaches to identifying and estimating, sources of inefficiency by means of artificially generated data, and (3) an extension of ordinary (linear programming) sensitivity analyses to deal with special features that require attention in DEA. Background is supplied in this introductory paper with accompanying proofs and explanations to facilitate understanding of what DEA provides in the way of underpinning for the papers that follow. An attempt is made to bring readers abreast of recent progress in DEA research and uses. A synoptic history is presented along with brief references to related work, and problems requiring attention are also indicated and possible research approaches also suggested.This research was partly supported by the National Science Foundation and USARI Contract MDA 903-83-K0312, with the Center for Cybernetic Studies, the University of Texas at Austin. It was also partly supported by the IC² Institute at the University of Texas at Austin. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.     

One-sided elasticities and technical efficiency in multi-output production: A theoretical framework

One of the concepts that have sparked considerable interest in the theory of production and efficiency is that of returns to scale (RTS). Economics researchers typically define RTS using the notion of elasticity. Considerable research activity on RTS has also been observed by management science researchers, who utilize the methodology of Data Envelopment Analysis (DEA) to gain insights on RTS. In this paper, we present a theoretical framework that integrates existing economics and management science literature on RTS, and provides a solid foundation for research work in this area. Our framework defines, discusses, and proposes an approach to measure input- and output-oriented elasticities, and one-sided RTS. We demonstrate how the work done in DEA is a special case of our framework, and discuss the conditions under which the resulting two left-hand, and the two right-hand elasticities can be equal. Future research directions are also discussed.     

带偏好DEA在“科学研究基金”管理中的应用研究

将带偏好锥DEA理论引入科学研究基金管理中,在包含"拥挤"迹象的生产可能集基础上建立了三个带偏好锥的平行网络结构DEA模型,对科研基金投入后产生的"成效"进行评价.这些模型分别从三个层面探讨了科研基金使用效率、分配合理性,以及最佳基金预算的确定方法.     

Comparing frontier methods for economic–environmental trade-off analysis

This paper uses a mechanistic frontier approach as a reference to evaluate the ability of conventional parametric (SFA) and non-parametric (DEA) frontier approaches for analyzing economic–environmental trade-offs. Conventional frontier approaches are environmentally adjusted through incorporating the materials balance principle. The analysis is worked out for the Flemish pig finishing case, which is both representative and didactic. Results show that, on average, SFA and DEA yield adequate economic–environmental trade-offs. Both methods are good estimators for technical efficiency. Cost allocative and environmental allocative efficiency scores are less robust, due to the well-known methodological advantages and disadvantages of SFA and DEA. For particular firms, SFA, DEA and the mechanistic approach may yield different economic–environmental trade-offs. One has therefore to be careful when using conventional frontier approaches for firm-specific decision support. The mechanistic approach allows for optimizing performances per average present finisher, which is the production unit in pig finishing. Conventional frontier methods do not allow for this optimization since the number of average present finishers varies along the production functions. Since the mechanistic production function is based on underlying growth, feed uptake and mortality functions, additional firm-specific indicators can also be calculated at each point of the production function.     

The Blackett Memorial Lecture 18 November 1997

It is argued that movement toward the ‘control’ aspects of management should be effected to expand OR/MS activities beyond their present (almost exclusive) emphasis on ‘planning’ functions. This will involve increasing the amount of empirical-inferential approaches to research (based on ex-post data) as one way to help bring this about. Examples of such empirical-inferential research activities in OR/MS are supplied by reference to the early (founding) work of PMS Blackett and others on high-level policy problems during World War II. Extensions to the control function are evidenced in the work of Robert Fetter and others in the development of Diagnostic Related Groups on which the Prospective Payment Systems are based with large and important impacts on the health care delivery systems in the USA as well as other countries. Other examples covered include the use of OR concepts in the early ‘turnaround’ of Federal Express from failure to success. Other new methods will nevertheless be needed to extend and improve presently available OR/MS approaches. Some of these possibilities are illustrated with Data Envelopment Analysis. Ways to combine DEA with commonly used statistical methods are described to show how new and old methods may be combined to further enhance their power and range. Similar relations of DEA to other OR/MS approaches are now being studied, some of which are presently occurring with ‘fuzzy sets’ and ‘multiple objective programming.’     

基于复合DEA和Malmquist指数的科技投入产出效率评价

本文利用非参数方法DEA对2004~2008年福建省9个地市的科技投入产出效率进行评价,并应用复合DEA方法和Malmquist指数来分析科技投入产出效率非DEA有效地区的形成原因及其生产力的动态变化。实证结果显示,福建省各市的科技效率总体呈上升趋势,但各地区科技的投入产出规模以及效率还存在着较大的差距,而其生产力的提高主要是技术效率所带来的贡献,技术进步则呈现大起大落的状态,技术进步对生产力的拉动仍需得到进一步加强与巩固,应加大科技研发投入和强化科技的引进创新,并注重消化吸收创新。     

军民融合企业技术转移效率区域差异及影响因素研究

在习近平新时代中国特色社会主义思想框架的指导下,军民融合已经上升为国家战略,技术转移作为军民两大板块多领域、全要素、深层次对接的重要载体,其转移效率直接影响到军民融合深度发展战略的实施。以2012~2016年间中国A股证券市场军民融合板块下45家企业的数据为基础,采用DEA的方法,通过测度不同区域技术转移效率,分析军民融合企业技术转移效率的区域差异并进行收敛性研究,进而通过面板 tobit模型分析以企业、政府、高校、环境四个方面产生的六个因素对军民融合企业技术转移效率的影响。研究结果表明:近五年军民融合企业技术转移效率波动较大,年际差异和省际差异都较为显著。军民融合企业自身规模、产品的差异化、政府的科技投入、技术市场成交额对技术转移效率有正向影响,高校数量、地区GDP对军民融合企业技术转移效率影响不显著。最后,提出相应的管理建议。     

DEA与数据挖掘

使用Wei和Yan给出的凸多面体的"和形式"与"交形式"相互转化的方法,得到"交形式"的生产可能集TWY,以及由此判别相对效率的方法,研究DEA用于数据挖掘,处理具有"海量"决策单元的相对效率评价(包括技术有效性和规模收益递增、不变、递减以及"拥挤"迹象).给出的方法只需使用一个"交形式"的生产可能集,与本作者先前的"DEA评测机"相比,可以节省很多计算量.方法是对DEA评测机的一种新的改进,是对数据挖掘领域的一个补充.     

基于三阶段DEA的独角兽上市企业创新效率评价

以中国64家独角兽上市企业为样本,采用三阶段DEA模型对独角兽企业的创新效率进行有效测算。结果表明,企业规模、成立年限、政府补贴、研发人员素质、外商直接投资和地区经济发展水平的提高有助于企业创新效率的提升,而产权性质、股权集中度则制约了企业创新效率的改进;清除环境影响和统计噪声后,多数企业的创新效率与纯技术效率上升,但仍处于较低水平。本文的实证结果有助于进一步提升独角兽企业的创新效率,也为独角兽企业后续的研究提供新的视角。     

Chapter 12 New uses of DEA and statistical regressions for efficiency evaluation and estimation — with an illustrative application to public secondary schools in Texas

This paper examines new combinations of Data Envelopment Analysis (DEA) and statistical approaches that can be used to evaluate efficiency within a multiple-input multiple-output framework. Using data on five outputs and eight inputs for 638 public secondary schools in Texas, unsatisfactory results are obtained initially from both Ordinary Least Squares (OLS) and Stochastic Frontier (SF) regressions run separately using one output variable at-a-time. Canonical correlation analysis is then used to aggregate the multiple outputs into a single aggregate output, after which separate regressions are estimated for the subsets of schools identified as efficient and inefficient by DEA. Satisfactory results are finally obtained by a joint use of DEA and statistical regressions in the following manner. DEA is first used to identify the subset of DEA-efficient schools. The entire collection of schools is then comprehended in a single regression with dummy variables used to distinguish between DEA-efficient and DEA-inefficient schools. The input coefficients are positive for the efficient schools and negative and statistically significant for the inefficient schools. These results are consistent with what might be expected from economic theory and are informative for educational policy uses. They also extend the treatments of production functions usually found in the econometrics literature to obtain one regression relation that can be used to evaluate both efficient and inefficient behavior.     

A surrogate based multi-fidelity approach for robust design optimization

Robust design optimization (RDO) is a field of optimization in which certain measure of robustness is sought against uncertainty. Unlike conventional optimization, the number of function evaluations in RDO is significantly more which often renders it time consuming and computationally cumbersome. This paper presents two new methods for solving the RDO problems. The proposed methods couple differential evolution algorithm (DEA) with polynomial correlated function expansion (PCFE). While DEA is utilized for solving the optimization problem, PCFE is utilized for calculating the statistical moments. Three examples have been presented to illustrate the performance of the proposed approaches. Results obtained indicate that the proposed approaches provide accurate and computationally efficient estimates of the RDO problems. Moreover, the proposed approaches outperforms popular RDO techniques such as tensor product quadrature, Taylor’s series and Kriging. Finally, the proposed approaches have been utilized for robust hydroelectric flow optimization, demonstrating its capability in solving large scale problems.     

基于改进DEA模型的科技投入产出有效性分析

合理地评价各地区的科技投入产出,对于资源的合理利用,提高资金的使用效率具有十分重要的现实意义.采用一种改进的DEA模型(简称M DEA),对2000—2002年间我国各地区的科技投入产出相对效率进行了充分评价和排序.并将三年的数据放在一起组成一个新的参考集,用同样的M DEA模型进行评估,得出各地区三年科技投入产出相对效率的变化情况.     

Effect of regulation on efficiency: evidence from Indian cement industry

The main objective of the paper is to analyze the impact of environmental regulation on technical efficiencies of Indian cement producing firms. It derives the technical efficiency (TE) scores of firms in the presence and absence of regulation and brings out the differences in their magnitudes in two scenarios: one in which the firms take initiatives to comply with the set standards by investing additional resources for pollution abatement and the other in which the firms do not take the necessary initiatives. The paper uses establishment level data from Annual Survey of Industries on cement for two years, the most recent data published for 2003–2004 and a previous year for 1999–2000 when the environmental regulations in India were in the initial phases of implementation. A non-parametric deterministic method of data envelopment analysis (DEA) is used to derive the TE scores of firms. The traditional DEA framework is modified by introducing weak disposability of bad outputs to characterize ‘effective environmental regulation’, which ensures that reducing pollution is not costless. For both years it has been found that the TE scores of firms under ‘effective regulation’ scenario are either higher than or equal to those derived under ‘ineffective regulation’ scenario resulting in a higher average TE at the industry level in the ‘effective regulation’ scenario.     

Context-dependent performance standards in DEA

Data envelopment analysis (DEA) is a mathematical approach to measuring the relative efficiency of peer decision making units (DMUs). It is particularly useful where no a priori information on the tradeoffs or relations among various performance measures is available. However, it is very desirable if “evaluation standards,” when they can be established, be incorporated into DEA performance evaluation. This is especially important when service operations are under investigation, because service standards are generally difficult to establish. The approaches that have been developed to incorporate evaluation standards into DEA, as reported in the literature, have tended to be rather indirect, focusing primarily on the multipliers in DEA models. This paper introduces a new way of building performance standards directly into the DEA structure when context-dependent activity matrixes exist for different classes of DMUs. For example, two sets of branches, whose transaction times are known to be different from each other, usually have two different activity matrixes. We develop a procedure so that a set of standard DMUs can be generated and incorporated directly into the DEA analysis. The proposed approach is applied to a sample of 100 branches of a major Canadian bank where different sets of time standards exist for three distinct groups of branches.     

Statistical inference for DEA estimators of directional distances

In productivity and efficiency analysis, the technical efficiency of a production unit is measured through its distance to the efficient frontier of the production set. The most familiar non-parametric methods use Farrell–Debreu, Shephard, or hyperbolic radial measures. These approaches require that inputs and outputs be non-negative, which can be problematic when using financial data. Recently, Chambers et al. (1998) have introduced directional distance functions which can be viewed as additive (rather than multiplicative) measures efficiency. Directional distance functions are not restricted to non-negative input and output quantities; in addition, the traditional input and output-oriented measures are nested as special cases of directional distance functions. Consequently, directional distances provide greater flexibility. However, until now, only free disposal hull (FDH) estimators of directional distances (and their conditional and robust extensions) have known statistical properties (Simar and Vanhems, 2012). This paper develops the statistical properties of directional d estimators, which are especially useful when the production set is assumed convex. We first establish that the directional Data Envelopment Analysis (DEA) estimators share the known properties of the traditional radial DEA estimators. We then use these properties to develop consistent bootstrap procedures for statistical inference about directional distance, estimation of confidence intervals, and bias correction. The methods are illustrated in some empirical examples.     

Recent Developments in Critical Management Science

For much of its history management science had a quantitative and technical emphasis. More recently, there has been a move towards more subjective approaches such as ‘soft OR’ and ‘soft systems’. Currently, there is interest in ‘critical management science’ drawing on critical theory, particularly the work of Habermas. This paper reviews developments in critical management science, in particular critiques of traditional and ‘soft’ management science; Jackson and Keys' system of systems methodology; critical management science methodologies and the problem of power in bringing about change; and the postmodernist critique.     

Methods based on data envelopment analysis for deriving group priorities in analytic hierarchy process

In recent years, group decision making has become one of the important issues in multiple criteria decision making, and analytic hierarchy process (AHP) is considered an appropriate method when dealing with this kind of problems. Many different approaches for attaining a group valuation in AHP have been developed. The applications most commonly employ the weighted geometric mean method. In the paper, we focus on the group AHP methods, which are based on the data envelopment analysis (DEA). First we discuss two methods for deriving a group priority vector: Wang and Chin’s DEA group method and Hosseinian et al.’s DEA-WDGD. Further, we propose a new WGMDEA method and compare all three methods with the WGMM on theoretical examples and on a real case study. The objective of the case study is to examine the current state of forest owners’ cooperatives. An analysis of the influence of forest owners’ cooperatives on private forest management in Slovenia was put forward. The A’WOT analysis, which is a combined method of AHP and SWOT analysis, an approach for identifying the strengths, weaknesses, opportunities and threats of the object under consideration, was performed.