New analytical hierarchical process/data envelopment analysis methodology for ranking decision‐making units

The analytical hierarchical process/data envelopment analysis (AHP/DEA) methodology for ranking decision‐making units (DMUs) has some problems: it illogically compares two DMUs in a DEA model; it is not compatible with DEA ranking in the case of multiple inputs/multiple outputs; and it leads to weak discrimination in cases where the number of inputs and outputs is large. In this paper, we propose a new two‐stage AHP/DEA methodology for ranking DMUs that removes these problems. In the first stage, we create a pairwise comparison matrix different from AHP/DEA methodology; the second stage is the same as AHP/DEA methodology. Numerical examples are presented in the paper to illustrate the advantages of the new AHP/DEA methodology.     

An AHP/DEA methodology for ranking decision making units

This paper presents a two-stage model for fully ranking organizational units where each unit has multiple inputs and outputs. In the first stage, the Data Envelopment Analysis (DEA) is run for each pair of units separately. In the second stage, the pairwise evaluation matrix generated in the first stage is utilized to rank scale the units via the Analytical Hierarchical Process (AHP). The consistency of this AHP/DEA evaluation can be tested statistically. Its goodness of fit with the DEA classification (to efficient/inefficient) can also be tested using non-parametric tests. Both DEA and AHP are commonly used in practice. Both have limitations. The hybrid model AHP/DEA takes the best of both models, by avoiding the pitfalls of each. The nonaxiomatic utility theory limitations of AHP are irrelevant here: since we are working with given inputs and outputs of units, no subjective assessment of a decision maker evaluation is involved. AHP/DEA ranking does not replace the DEA classification model, rather it furthers the analysis by providing full ranking in the DEA context for all units, efficient and inefficient.     

Sensitivity analysis of the additive model in data envelopment analysis while inputs and outputs are fuzzy data

Data envelopment analysis (DEA) requires input and output data to be precisely known. This is not always the case in real applications. Sensitivity analysis of the additive model in DEA is studied in this paper while inputs and outputs are symmetric triangular fuzzy numbers. Sufficient conditions for simultaneous change of all outputs and inputs of an efficient decision-making unit (DMU) which preserves efficiency are established. Two kinds of changes on inputs and outputs are considered. For the first state, changes are exerted on the core and margin of symmetric triangular fuzzy numbers so that the value of inputs increase and the value of outputs decrease. In the second state, a non-negative symmetric triangular fuzzy number is subtracted from outputs to decrease outputs and it is added to inputs to increase inputs. A numerical illustration is provided.     

A new network epsilon-based DEA model for supply chain performance evaluation

Supply chain performance evaluation problems are inherently complex problems with multilayered internal linking activities and multiple entities. Data Envelopment Analysis (DEA) has been used to evaluate the relative performance of organizational units called Decision Making Units (DMUs). However, the conventional DEA models cannot take into consideration the complex nature of supply chains with internal linking activities. Network DEA models using radial measures of efficiency are used for supply chain performance evaluation problems. However, these models are not suitable for problems where radial and non-radial inputs and outputs must be considered simultaneously. DEA models using Epsilon-Based Measures (EBMs) of efficiency are proposed for a simultaneous consideration of radial and non-radial inputs and outputs. We extend the EBM model and propose a new Network EBM (NEBM) model. The proposed NEBM model combines the radial and non-radial measures of efficiency into a unified framework for solving network DEA problems. A case study is presented to exhibit the efficacy of the procedures and to demonstrate the applicability of the proposed method to a supply chain performance evaluation problem in the semiconductor industry.     

Evaluation and ranking DMUs in the presence of both undesirable and ordinal factors in data envelopment analysis

In the last decade,ranking units in data envelopment analysis(DEA) has become the interests of many DEA researchers and a variety of models were developed to rank units with multiple inputs and multiple outputs.These performance factors(inputs and outputs) are classified into two groups:desirable and undesirable.Obviously,undesirable factors in production process should be reduced to improve the performance.Also,some of these data may be known only in terms of ordinal relations.While the models developed in the past are interesting and meaningful,they didn t consider both undesirable and ordinal factors at the same time.In this research,we develop an evaluating model and a ranking model to overcome some deficiencies in the earlier models.This paper incorporates undesirable and ordinal data in DEA and discusses the efficiency evaluation and ranking of decision making units(DMUs) with undesirable and ordinal data.For this purpose,we transform the ordinal data into definite data,and then we consider each undesirable input and output as desirable output and input,respectively.Finally,an application that shows the capability of the proposed method is illustrated.     

Data envelopment analysis of integer-valued inputs and outputs

This paper addresses DEA scenarios whose inputs and outputs are naturally restricted to take integer values. Conventional DEA models would project the DMU onto targets that generally do not respect such type of integrality constraints. Although integer-valued inputs and outputs can be considered as a special case of ordinal inputs and outputs, the use of that type of models has many drawbacks. In this paper a MILP DEA model that guarantees the required integrality of the computed targets is proposed.     

A concept of fuzzy input mix-efficiency in fuzzy DEA and its application in banking sector

Data envelopment analysis (DEA) is a linear programming based non-parametric technique for evaluating the relative efficiency of homogeneous decision making units (DMUs) on the basis of multiple inputs and multiple outputs. There exist radial and non-radial models in DEA. Radial models only deal with proportional changes of inputs/outputs and neglect the input/output slacks. On the other hand, non-radial models directly deal with the input/output slacks. The slack-based measure (SBM) model is a non-radial model in which the SBM efficiency can be decomposed into radial, scale and mix-efficiency. The mix-efficiency is a measure to estimate how well the set of inputs are used (or outputs are produced) together. The conventional mix-efficiency measure requires crisp data which may not always be available in real world applications. In real world problems, data may be imprecise or fuzzy. In this paper, we propose (i) a concept of fuzzy input mix-efficiency and evaluate the fuzzy input mix-efficiency using α – cut approach, (ii) a fuzzy correlation coefficient method using expected value approach which calculates the expected intervals and expected values of fuzzy correlation coefficients between fuzzy inputs and fuzzy outputs, and (iii) a new method for ranking the DMUs on the basis of fuzzy input mix-efficiency. The proposed approaches are then applied to the State Bank of Patiala in the Punjab state of India with districts as the DMUs.     

Fuzzy stochastic data envelopment analysis with application to base realignment and closure (BRAC)

Data envelopment analysis (DEA) is a non-parametric method for evaluating the relative efficiency of decision-making units (DMUs) on the basis of multiple inputs and outputs. Conventional DEA models assume that inputs and outputs are measured by exact values on a ratio scale. However, the observed values of the input and output data in real-world problems are often vague or random. Indeed, decision makers (DMs) may encounter a hybrid uncertain environment where fuzziness and randomness coexist in a problem. Several researchers have proposed various fuzzy methods for dealing with the ambiguous and random data in DEA. In this paper, we propose three fuzzy DEA models with respect to probability-possibility, probability-necessity and probability-credibility constraints. In addition to addressing the possibility, necessity and credibility constraints in the DEA model we also consider the probability constraints. A case study for the base realignment and closure (BRAC) decision process at the U.S. Department of Defense (DoD) is presented to illustrate the features and the applicability of the proposed models.     

Modeling fuzzy data envelopment analysis by parametric programming method

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiency of decision making units (DMUs) consuming the same types of inputs and producing the same types of outputs. This paper studies the DEA models with type-2 data variations. In order to deal with the existed type-2 fuzziness, we propose the mean reduction methods for type-2 fuzzy variables. Based on the mean reductions of the type-2 fuzzy inputs and outputs, we formulate a new class of fuzzy generalized expectation DEA models. When the inputs and outputs are mutually independent type-2 triangular fuzzy variables, we discuss the equivalent parametric forms for the constraints and the generalized expectation objective, where the parameters characterize the degree of uncertainty of the type-2 fuzzy coefficients so that the information cannot be lost via our reduction method. For any given parameters, the proposed model becomes nonlinear programming, which can be solved by standard optimization solvers. To illustrate the modeling idea and the efficiency of the proposed DEA model, we provide one numerical example.     

Allocating fixed resources and setting targets using a common-weights DEA approach

Data envelopment analysis (DEA) is a data-driven non-parametric approach for measuring the efficiency of a set of decision making units (DMUs) using multiple inputs to generate multiple outputs. Conventionally, DEA is used in ex post evaluation of actual performance, estimating an empirical best-practice frontier using minimal assumptions about the shape of the production space. However, DEA may also be used prospectively or normatively to allocate resources, costs and revenues in a given organization. Such approaches have theoretical foundations in economic theory and provide a consistent integration of the endowment-evaluation-incentive cycle in organizational management. The normative use, e.g. allocation of resources or target setting, in DEA can be based on different principles, ranging from maximization of the joint profit (score), combinations of individual scores or game-theoretical settings. In this paper, we propose an allocation mechanism that is based on a common dual weights approach. Compared to alternative approaches, our model can be interpreted as providing equal endogenous valuations of the inputs and outputs in the reference set. Given that a normative use implicitly assumes that there exists a centralized decision-maker in the organization evaluated, we claim that this approach assures a consistent and equitable internal allocation. Two numerical examples are presented to illustrate the applicability of the proposed method and to contrast it with earlier work.     

Assessing the efficiency of supply chain scheduling algorithms using data envelopment analysis

Where different supply chain planning algorithms are used, generally similar results may pose some challenges on the differentiating powers of evaluating different production schedules because of the increasing complexity of a supply chain network structure. For the comparison purpose, performance evaluation of different supply chain planning algorithms aims to use different supply chains models with different demands, capacities, and commonality through efficiency perspective by using a modified network rational data envelopment analysis (DEA) model. The proposed DEA model has the abilities: (1) to treat only undesirable outputs that exist without normal output, and the situation where input and output are both zero by introducing two new parameters to denote the maximum inventory and amount of delayed demands of a given node in a given time period; and (2) to evaluate the effect of the undesirable outputs/inputs on efficiency with assumption that they leave the system at the end of the current time period and re-enter the system at the beginning of the next time period. To prove the effectiveness of this DEA model, eighteen scenarios with different demands, capacities, and multiple periods are compared. In addition, this study tests the DEA model on a wafer testing/probing operation of a leading global semiconductor manufacturing and testing company in Taiwan by internal supply chain perspective. Results show that the DEA model proposed in this study can be used to assess the efficiency of a real-world operation with undesirable outputs/inputs, such as inventory and delayed demands.     

A generalized multiple layer data envelopment analysis model for hierarchical structure assessment: A case study in road safety performance evaluation

Data envelopment analysis (DEA) is a powerful analytical research tool for measuring the relative efficiency of a homogeneous set of decision making units (DMUs) by obtaining empirical estimates of relations between multiple inputs and multiple outputs related to the DMUs. To further embody multilayer hierarchical structures of these inputs and outputs in the DEA framework, which are prevalent in today’s performance evaluation activities, we propose a generalized multiple layer DEA (MLDEA) model. Starting from the input-oriented CCR model, we elaborate the mathematical deduction process of the MLDEA model, formulate the weights in each layer of the hierarchy, and indicate different types of possible weight restrictions. Meanwhile, its linear transformation is realized and further extended to the BCC form. To demonstrate the proposed MLDEA model, a case study in evaluating the road safety performance of a set of 19 European countries is carried out. By using 13 hierarchical safety performance indicators in terms of road user behavior (e.g., inappropriate or excessive speed) as the model’s input and 4 layered road safety final outcomes (e.g., road fatalities) as the output, we compute the most optimal road safety efficiency score for the set of European countries, and further analyze the weights assigned to each layer of the hierarchy. A comparison of the results with the ones from the one layer DEA model clearly indicates the usefulness and effectiveness of this improvement in dealing with a great number of performance evaluation activities with hierarchical structures.     

Fuzzy dynamic multi-objective Data Envelopment Analysis model

Data Envelopment Analysis (DEA) is a managerial powerful tool to evaluate the relative efficiency of each decision making unit (DMU). Nowadays, multi-objective DEA models in static environment are an attractive technique for evaluation quantity and quality aspects of performance analysis because there is some weakness in single objective DEA such as one-dimensional performance analysis and also it is important to consider the decision maker(s) preference over the potential adjustments of various inputs and outputs when DEA is employed. In this paper, a fuzzy dynamic multi-objective DEA model is presented in which data are changing sequentially. This paper assesses the performance of the railways using presented model as a numerical example to evaluate the results of the model. Results indicate that the multiple objective program model improves discriminating power of classical DEA models with just one time calculation of the efficiency achievement for all DUMs.     

Slacks-based measures of efficiency in imprecise data envelopment analysis: An approach based on data envelopment analysis with double frontiers

Data envelopment analysis (DEA) is a mathematical approach for evaluating the efficiency of decision-making units (DMUs) that convert multiple inputs into multiple outputs. Traditional DEA models assume that all input and output data are known exactly. In many situations, however, some inputs and/or outputs take imprecise data. In this paper, we present optimistic and pessimistic perspectives for obtaining an efficiency evaluation for the DMU under consideration with imprecise data. Additionally, slacks-based measures of efficiency are used for direct assessment of efficiency in the presence of imprecise data with slack values. Finally, the geometric average of the two efficiency values is used to determine the DMU with the best performance. A ranking approach based on degree of preference is used for ranking the efficiency intervals of the DMUs. Two numerical examples are used to show the application of the proposed DEA approach.     

Benchmarking of service quality with data envelopment analysis

This paper proposes a data envelopment analysis (DEA) approach to measurement and benchmarking of service quality. Dealing with measurement of overall service quality of multiple units with SERVPERF as multiple-criteria decision-making (MCDM), the proposed approach utilizes DEA, in particular, the pure output model without inputs. The five dimensions of SERVPERF are considered as outputs of the DEA model. A case study of auto repair services is provided for the purpose of illustration. The current practice of benchmarking of service quality with SERVQUAL/SERVPERF is limited in that there is little guidance to whom to benchmark and to what degree service quality should be improved. This study contributes to the field of service quality benchmarking by overcoming the above limitations, taking advantage of DEA’s capability to handle MCDM problems and provide benchmarking guidelines.     

考虑中间变量产出时滞性的两阶段评价

传统DEA模型假设特定时期的产出是通过消耗同一时期的投入产生的,这个潜在的假设不适用于某些绩效评价,即一个特定时期的产出不仅需要消耗该时期的投入,而且需要消耗之前多个时期的投入。为了更加客观地评价两阶段过程的效率值,构建了考虑中间变量产出时滞性的两阶段DEA模型,同时将其与Malmquist生产率指数相结合,寻求时间序列上的动态变化,从而找到效率变化的原因。并将提出的方法应用到中国30个省份创新效率的评价中,结果表明,考虑中间变量产出时滞性的模型排名更客观;创新效率不仅与研发阶段和经济转化阶段的效率密切相关,而且还受外部因素的影响。     

Additive centralized and Stackelberg DEA models for two‐stage system with shared resources

Data envelopment analysis (DEA) is a nonparametric programming method for evaluating the efficiency performance of decision making units (DMUs) with multiple inputs and outputs. The classic DEA model cannot provide accurate efficiency measurement and inefficiency sources of DMUs with complex internal structure. The network DEA approach opens the “black box” of DMU by taking its internal operations into consideration. The complexities of DMU's internal structure involve not only the organization of substages, but also the inputs allocation and the operational relations among the individual stages. This paper proposes a set of additive DEA models to evaluate and decompose the efficiency of a two‐stage system with shared inputs and operating in cooperative and Stackelberg game situations. Under the assumptions of cooperative and noncooperative gaming, the proposed models are able to highlight the effects of strategic elements on the efficiency formation of DMUs by calculating the optimal proportion of the shared inputs allocated to each stage. The case of information technology in the banking industry at the firm level, as discussed by Wang, is revisited using the developed DEA approach.     

Evaluating the efficiency of a two-stage production process using data envelopment analysis

Data envelopment analysis (DEA) has been widely used to evaluate the comparative efficiencies of production processes. Most of the DEA applications assume that production processes consist of one stage. However, many production processes such as IT investments have more than one stage. In a two‐stage production process, the first stage inputs produce intermediate outputs, which are used as inputs to the second stage to produce the final outputs. In such cases, using single‐stage DEA may result in inaccurate efficiency evaluation. To address such problems, DEA models assuming two‐stage production processes have been developed. In this paper, we extend two‐stage DEA models by considering input and output slacks. We apply our model to the data from the banking industry and compare the results with those of the previous two‐stage DEA models. Our model can identify weakly efficient units of evaluation that could not be identified by the previous models.     

A study of the relative efficiency of Chinese ports: a financial ratio‐based data envelopment analysis approach

Abstract: This research examines the relative efficiency of 11 major Chinese ports by using an innovative adopted version of Data Envelopment Analysis (DEA). DEA is a non‐parametric approach to weigh the inputs/outputs and measure the relative efficiency of decision‐making units. This paper adopts an output‐oriented version of DEA based on financial ratios in which no inputs are utilized. The new adopted DEA model provides a rounded judgement on port efficiency taking into consideration multiple financial ratios simultaneously and combining them into a single measure of efficiency. The mathematical model is solved for every port, and the relative efficiency of each port is determined. The results of DEA show that the higher a port's efficiency ratio in relation to the corresponding ratio of another port, the higher the efficiency of this port. Finally, suggestions based on the data analysis are provided for managerial decision makers to improve the areas needed for port operating efficiency.     

Data Envelopment Analysis Based on Choquet Integral

Data envelopment analysis (DEA) is a widely used technique in decision making. The existing DEA models always assume that the inputs (or outputs) of decision‐making units (DMUs) are independent with each other. However, there exist positive or negative interactions between inputs (or outputs) of DMUs. To reflect such interactions, Choquet integral is applied to DEA. Self‐efficiency models based on Choquet integral are first established, which can obtain more efficiency values than the existing ones. Then, the idea is extended to the cross‐efficiency models, including the game cross‐efficiency models. The optimal analysis of DEA is further investigated based on regret theory. To estimate the ranking intervals of DMUs, several models are also established. It is founded that the models considering the interactions between inputs (or outputs) can obtain wider ranking intervals.