DEA cross-efficiency evaluation based on satisfaction degree: an application to technology selection

Data envelopment analysis (DEA) has been extended to cross-efficiency evaluation to provide better discrimination and ranking of decision-making units (DMUs). However, the non-uniqueness of optimal weights in the traditional DEA models (CCR and BCC models) has reduced the usefulness of the DEA cross-efficiency evaluation method. To solve this problem, we introduce the concept of the satisfaction degree of a DMU towards a set of optimal weights for another DMU. Then, a new DEA cross-efficiency evaluation approach, which contains a maxmin model and two algorithms, is proposed based on the satisfaction degrees of the DMUs. Our maxmin model and algorithm 1 can obtain for each DMU an optimal set of weights that maximises the least satisfaction degrees among all the other DMUs. Further, our algorithm 2 can then be used to guarantee the uniqueness of the optimal weights for each DMU. Finally, our approach is applied to a real-world case study of technology selection.     

Using common weights and efficiency invariance principles for resource allocation and target setting

Data envelopment analysis (DEA) has proven to be a useful technique for evaluating the relative performance of comparable and homogeneous decision-making units (DMUs). In recent years, DEA-based resource allocation and target setting approaches have gained more and more attention from both practitioners and academic researchers. In this paper, we propose a new mechanism to simultaneously adopt the principles of common weights and efficiency invariance in allocating multiple resources and setting multiple targets among DMUs. To obtain the final plan, we minimise the deviation between the possible plan based on common weights and another feasible plan emphasising efficiency invariance. If the minimum deviation equals zero, one optimal plan will be determined. In general situations, however, the proposed approach will present two plans that have a non-zero deviation. One is generated using a common set of weights for all DMUs in such a way that the change of efficiencies is minimised, while the other is generated by strictly keeping efficiency scores unchanged yet having similar or even identical weights on input–output measures for each DMU to the utmost extent. The efficacy and usefulness of the proposed approach are demonstrated using a numerical example from previous literature and an empirical application to an urban bus company in China.     

Building performance standards into data envelopment analysis structures

Data Envelopment Analysis (DEA) is a mathematical approach to measuring the relative efficiency of peer Decision-Making Units (DMUs). DEA is particularly useful where no a priori information on the trade-offs 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 particularly important when service operations are under investigation, because service standards are generally difficult to establish. A number of approaches have been developed to incorporate evaluation standards into DEA as reported in the literature. These approaches tend to be rather indirect, focusing primarily on the multipliers in the DEA models. This paper introduces a new way of building performance standards directly into the DEA structure. Based upon the conventional DEA model and an activity matrix, 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 time standards are used to generate a set of standard bank branches.     

An innovation funnel process for set-based conceptual design via DOE exploration,DEA selection and computer simulation

This paper presents a conceptual design approach including pattern creation from designers, alternative exploration with a DOE matrix, alternative analysis via computer simulation and alternative selection by DEA analysis. Designers possessing domain knowledge create various design patterns to meet the requirements of product performance and customer expectations. Then, based on these design patterns, the alternatives, considered as decision-making units (DMUs), are extracted from various quality level combinations by following the use of the DOE matrix. The nature of the DOE matrix ensures that distinctive representatives are constructed for all design alternatives. The total alternatives (DMUs) consist of the alternatives associated with all the patterns. Computer simulation with ANSYS software is introduced to convert the quality level combination of each alternative (DMU) into simulated outputs, which are further categorised into DEA inputs and DEA outputs for DEA frontier analysis. Four DEA methods, CCR-min input, CCR-max output, BCC-min input and BCC-max output, are used for analysing typical market representatives resulting from market uncertainty. The found efficiencies are used to rank and select the explored alternatives (DMUs) for the next stage of the detailed design. A bike-frame product is chosen as an example to demonstrate the proposed approach. The results clearly show that the proposed approach enables designers to economically select appropriate design alternatives that satisfy performance expectations during the conceptual design stage.     

模糊权重约束的DEA模型及其应用

基于Zadeh模糊优越集定义,应用模糊权重约束DEA模型对医院服务效率进行评价.通过最大化模糊隶属函数来确定投入与产出权重的上限和下限,以避免传统DEA模型中权重为0的缺陷.实例选取期末实有床位数和医护人员数为两个投入变量,总诊疗人次和总出院人次为两个产出变量,评价广州市15所医院的相对服务效率.评价结果对医院管理决策更具客观性和实用性.     

Methods and applications of DEA cross-efficiency: Review and future perspectives

The field of engineering management usually involves evaluation issues, such as program selection, team performance evaluation, technology selection, and supplier evaluation. The traditional self-evaluation data envelopment analysis (DEA) method usually exaggerates the effects of several inputs or outputs of the evaluated decision-making unit (DMU), resulting in unrealistic results. To address this problem, scholars have proposed the cross-efficiency evaluation (CREE) method. Compared with the DEA method, CREE can rank DMUs more completely by using reasonable weights. With the extensive application of this technique, several problems, such as non-unique weights and non-Pareto optimal results, have arisen in CREE methods. Therefore, the improvement of CREE has attracted the attention of many scholars. This paper reviews the theory and applications of CREE, including the non-uniqueness problem, the aggregation of cross-efficiency data, and applications in engineering management. It also discusses the directions for future research on CREE.     

Developing a new chance constrained NDEA model to measure the performance of humanitarian supply chains

Data envelopment analysis (DEA) is a method for measuring performance of decision making units (DMUs). Conventional DEA models view DMUs as black boxes. Network DEA (NDEA) models have been developed to overcome this shortfall. This paper develops a new NDEA model based on modified enhanced Russell measure model. This paper measures performance of humanitarian supply chains (HSCs) by an NDEA model. Capabilities of the proposed model are addressed by theorems. However, in the real world, there might be stochastic data. This paper presents a stochastic version of the proposed NDEA model to measure the performance of HSCs. We analyse main properties of our model. We present a case study to demonstrate the applicability of the proposed model.     

DEA based on strongly efficient and inefficient frontiers and its application on port efficiency measurement

Data envelopment analysis (DEA) is a non-parametric analytical methodology widely used in efficiency measurement of decision making units (DMUs). Conventionally, after identifying the efficient frontier, each DMU is compared to this frontier and classified as efficient or inefficient. This paper first introduces the strongly efficient frontier (SEF) and strongly inefficient frontier (SIF), and then proposes several models to calculate various distances between DMUs and both frontiers. Specifically, the distances considered in this paper include: (1) both the distance to SEF and the distance to SIF, where the former reveals a unit’s potential opportunity to become a best performer while the latter reveals its potential risk to become a worst performer, and (2) both the closest distance and the farthest distance to frontiers, which may provide different valuable benchmarking information for units. Subsequently, based on these distances, eight efficiency indices are suggested to rank DMUs. Due to different distances adopted in these indices, the efficiency of units can be evaluated from diverse perspectives with different indices employed. In addition, all units can be fully ranked by these indices. The efficiency of 24 major Asian container ports is analyzed with our study, where the potential opportunities and potential crises of these ports are revealed and some new insights about their efficiency are provided.     

Measuring the R&D efficiency of regions by a parallel DEA game model

This paper proposes a model that can measure the R&D efficiency of each region (DMU) or each production unit while taking the inter-DMU competition and inter-subprocesses competition into account. The game cross-efficiency concept is introduced into the parallel DEA model. Furthermore, each DMU (subprocess) tries to maximize its own efficiency without harming the cross efficiency of each of the other DMUs (subprocess). We carry out an algorithm to obtain the best game cross-efficiency scores. This score has been proved to converge to a Nash equilibrium point. We use the proposed model to measure the R&D efficiency of the 30 provinces of China. The results show that the algorithm converges to a unique cross efficiency and our model indeed takes the bargaining power of DMUs and subprocesses into account.     

An improved MCDM DEA model for technology selection

This paper presents an Improved MCDM Data Envelopment Analysis (DEA) model in order to evaluate the best efficient DMUs in Advanced Manufacturing Technology (AMT). This model is capable of ranking the next most efficient DMUs after removing the previous best one.     

A new DEA common-weight multi-criteria decision-making approach for technology selection

This paper addresses an advanced manufacturing technology selection problem by proposing a new common-weight multi-criteria decision-making (MCDM) approach in the evaluation framework of data envelopment analysis (DEA). We improve existing technology selection models by giving a new mathematical formulation to simplify the calculation process and to ensure its use in more general situations with multiple inputs and multiple outputs. Further, an algorithm is provided to solve the proposed model based on mixed-integer linear programming and dichotomy. Compared with previous approaches for technology selection, our approach brings new contributions. First, it guarantees that only one decision-making unit (DMU) (referring to a technology) can be evaluated as efficient and selected as the best performer while maximising the minimum efficiency among all the DMUs. Second, the number of mixed-integer linear programs to solve is independent of the number of candidates. In addition, it guarantees the uniqueness of the final optimal set of common weights. Two benchmark instances are used to compare the proposed approach with existing ones. A computational experiment with randomly generated instances is further proceeded to show that the proposed approach is more suitable for situations with large datasets.     

Data envelopment analysis of AGV fleet sizing at a port container terminal

A decision-making approach based on Data Envelopment Analysis (DEA) for determining the efficient container handling processes (considering the number of employed Automated Guided Vehicles (AGVs)) at a port container terminal (PCT) is presented in this paper. Containers are unloaded from the ship by quay cranes and transported to the storage area by AGVs. We defined performance measures of proposed container handling processes and analysed the effects when changing the number of AGVs. The values of performance measures were collected and/or calculated from simulation. Container handling process, with a fixed number of quay cranes, when a different number of AGVs is used to transport containers from berth to assigned locations within storage area, represents a decision-making unit (DMU). We applied the basic CCR (Charnes, Cooper and Rhodes) DEA model with two inputs: average ship operating delay costs and average operating costs of employed equipment at a PCT, and two outputs: average number of handled import containers per ship and weighted average utilisation rate of equipment at a PCT. DEA method proved to be useful when testing different DMUs and when determining efficient DMUs for planning purposes. This study shows that efficiency evaluation of AGV fleet sizing and operations is useful for planning purposes at PCTs.     

MODELS FOR IMPROVED EFFECTIVENESS BASED ON DEA EFFICIENCY RESULTS

Following the characterization via Data Envelopment Analysis (DEA) of managerial units as efficient or inefficient, management will wish to increase profitability and/or control costs while becoming (or remaining) technically efficient in the DEA sense. This paper presents three families of models for achieving this and describes the managerial situations in which they are useful. The first addresses the management of an existing Decision Making Unit (DMU) and die second attempts to identify the desired “location” for a new DMU. The third addresses the aggregate of all DMUs, reallocating scarce resources among them for maximum overall organizational profitability and technical efficiency.     

DEA cross-efficiency aggregation method based upon Shannon entropy

Existing approaches for DEA 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 Decision Making Unit (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 Shannon entropy for cross-efficiency aggregation. In the study, we propose an entropy model to generate a set of weights for aggregating and determining the ultimate cross-efficiency instead of the traditional average cross-efficiency. We prove that the set of weight is a unique global optimal solution which can reflect the goodness of this method. Finally, two examples of a flexible manufacturing system and 27 industrial robots are illustrated to examine the validity of the proposed method.     

基于DEA的汽车工业企业投资有效性分析

运用数据包络分析方法，建立了我国主要汽车制造企业投资相对有效性的评价模型。该模型测算了各企业的总体效率、纯技术效率、纯规模效率及其规模效益状况，并且利用“投影”分析，对非DEA有效的决策单元(DMU)的投入产出值进行了调整，使之达到相对有效。文章进而结合DEA改进值，对非DEA有效的企业提出使其达到DEA有效的可行措施，同时分析了企业经营效率与资源配置效率之间的关系，为企业管理者进行科学决策提供依据和参考。     

A robust optimization approach to overall profit efficiency with data uncertainty: application on bank industry

In this paper, we consider a framework of data envelopment analysis (DEA) to measure the overall profit efficiency of decision-making units (DMUs) subject to inputs and outputs uncertainty. Under uncertain conditions, classic methods can lead to unrealistic solutions in practice. In this work, robust optimization is proposed to incorporate uncertainty into measuring the overall profit efficiency. In a robust optimization model, it is supposed that uncertain parameters belong to a specified set with a solution that is efficient for all possible uncertainty outcomes while it is not optimal for a given value of the parameters. We show that the overall profit efficiency score may not always occur in an optimistic case and the decision maker can obtain the overall profit efficiency score corresponding to a value in the uncertainty set. The results of the experiment on bank data show that a robust overall profit efficiency score provides a significant improvement in the performance, as the uncertainty increases.

Abbreviations: DEA: data envelopment analysis; DMUs: decision-making units; CRS: constant returns to scale; VRS: variable returns to scale; ROP: robust optimization problem; RC: robust counterpart; ROPE: robust overall profit efficiency; OOPE: optimistic overall profit efficiency; GAMS: generalized algebraic modeling system     

Convex cone-based ranking of decision-making units in DEA

OR Spectrum - One of the major research streams in data envelopment analysis (DEA) is ranking decision-making units (DMUs). Utilizing a multicriteria decision-making technique, we develop a novel...     

Dual-role factors in data envelopment analysis

This paper presents a methodology for dealing with performance evaluation settings where factors can simultaneously play both input and output roles. Model structures are developed for classifying Decision-Making Units (DMUs) into three groups according to whether such a factor is behaving like an output, an input, or is in equilibrium, neither wanting to lose or gain any of the factors. We connect these ideas to those involving increasing, decreasing and constant returns to scale. Examples of factors that play this dual-role are: trainees in organizations, such as nurses, medical students, and doctoral students; awards to scholars or university departments; certain revenue—generating transactions in banks, and so on. We apply the model to the analysis of a set of university departments. In some settings, a dual-role factor may be one that can be reallocated, such as would be the case when DMUs are managed by a central authority. We develop the appropriate model structures to permit such a reallocation. We present two such structures, with the first involving reallocation from an existing allocation, and the second, a zero-base allocation.     

Evaluating and selecting investments in industrial robots

This paper proposes an alternative methodology for the selection of industrial robots using data envelopment analysis (DEA). It aims at the identification, in a cost/benefit perspective, of the optimal robot, by measuring, for each robot, the relative efficiency through the resolution of linear programming problems. The methodology adopted is based on a sequential dual use of DEA with restricted weights. This approach increases the discriminatory power of standard DEA and makes it possible to achieve a better balancing of robot performances. Further benefits refer to the possibility of extending the use of this approach to various multi-attribute decision-making problems where each performance may depend on a number of factors. An empirical application of the methodology, using data from 12 robot manufacturers, confirms the applicability of revised DEA to advanced manufacturing technology selection, and reinforces its use as a tactical/operational tool in the area of production/operations. In order to evaluate the overall balancing of robot performance indicators, a sensitivity analysis (with variable weight restrictions) is also carried out. The comparison of the results with those obtained by applying cross-efficiency, another DEA-based methodology (Baker and Talluri 1997 Computers and Industrial Engineering , 32 , 101- 108), is also addressed and discussed. Finally, the dual model of DEA has helped to provide a useful economical and technological analysis of the inefficient robots.     

Supplier evaluation and selection: an augmented DEA approach

Evaluating and selecting suppliers is an essential part of effectively managing today's dynamic and global supply chains. In this paper, we propose a supplier evaluation and selection methodology based on an extension of data envelopment analysis (DEA) that can evaluate suppliers in an efficient manner. Through the incorporations of a range of virtual standards, the proposed methodology termed augmented DEA, has enhanced discriminatory power over basic DEA models to rank suppliers. In addition, weight constraints are introduced to reduce the possibility of having inappropriate input and output factor weights. We demonstrate the application of augmented DEA with comparison experiments and find that the augmented DEA model has advantages over the basic DEA model as well as the cross-efficiency and super-efficiency models. Finally, we present a case application with data obtained from a communication and aviation electronics company to demonstrate the applicability and use of augmented DEA.