Measuring congestion in sustainable supply chain based on data envelopment analysis

Neural Computing and Applications - Sustainable Supply Chain Management (SSCM) involves the integrating of environmental, social and economic concerns into supply chain management activities with...     

Evaluation method based on ranking in data envelopment analysis

Data envelopment analysis (DEA) has been developed as a method to evaluate efficiency of Decision Making Unit (DMU). In order to analyze DMU in detail, each DEA model is formulated as a mathematical programming problem utilizing the values of inputs and outputs of all DMUs as coefficients. Each DMU is evaluated by a different weight. Then, the efficiency score of each DMU is determined by using an advantageous weight for itself. In general, the efficiency score is obtained by selecting the most advantage weight. In some real cases, seeking the best ranking is sometimes more important than maximizing the efficiency score.In this paper, we propose a model called rank-based measure (RBM) to evaluate DMU from a different standpoint. We suggest a method to obtain a weight which gives the best ranking, and calculates a weight between maximizing the efficiency score and keeping the best ranking. In order to calculate an efficiency score and the best ranking, we repeatedly solve linear programming problems. Moreover, we apply RBM model to the cross efficiency evaluation. Furthermore, a numerical experiment is shown to compare the rankings and scores with traditional evaluations.     

Optimal direct mailing modelling based on data envelopment analysis

Data envelopment analysis (DEA) is a mathematical programming technique that is frequently used for measuring and benchmarking efficiency of the homogenous decision‐making units (DMUs). This paper proposes a new use of DEA for customers scoring and particularly their direct mailing modelling. Moreover, because DEA models suffer from some weaknesses, that is, unrealistic weighting scheme of the inputs and outputs and incomplete ranking among efficient DMUs, the present paper compares different ways of solving these problems and concludes that common set of weights method, as a result of some advantages, outperforms other procedures.     

Cross efficiency evaluation method based on weight-balanced data envelopment analysis model

In this paper, the cross efficiency evaluation method, regarded as a DEA extension tool, is firstly reviewed for its utilization in identifying the Decision Making Unit (DMU) with the best practice and ranking the DMUs by their respective cross-efficiency scores. However, we then point out that the main drawback of the method lies in non-uniqueness of cross-efficiency scores resulted from the presence of alternate optima in traditional DEA models, obviously making it become less effective. Aiming at the research gap, a weight-balanced DEA model is proposed to lessen large differences in weighted data (weighted inputs and weighted outputs) and to effectively reduce the number of zero weights for inputs and outputs. Finally, we use two examples of the literature to illustrate the performance of this approach and discuss some issues of interest regarding the choosing of weights in cross-efficiency evaluations.     

A new method based on the dispersion of weights in data envelopment analysis

One of the drawbacks of the data envelopment analysis (DEA) is the problem of lack of discrimination among efficient decision making units (DMUs) and hence yielding many numbers of DMUs as efficient. The main purpose of this study is to overcome this inability. In the case in which the minimization of the coefficient of variation (CV) for input–output weights is added to the DEA model, more reasonable and more homogeneous input–output weights are obtained. For this new proposed model based on the CV it is observed that the number of efficient DMUs is reduced, improving the discrimination power. When this new approach is applied to two well-known examples in the literature, and a real-world data of OECD countries, it has been seen that the new model yielded a more balanced dispersion of input–output weights and reduced the number of efficient DMUs. In addition, the applicability of the new model is tested by a simulation study.     

An ideal-seeking fuzzy data envelopment analysis framework

Data envelopment analysis (DEA) is a widely used mathematical programming approach for evaluating the relative efficiency of decision making units (DMUs) in organizations. Crisp input and output data are fundamentally indispensable in traditional DEA evaluation process. However, the input and output data in real-world problems are often imprecise or ambiguous. In this study, we present a four-phase fuzzy DEA framework based on the theory of displaced ideal. Two hypothetical DMUs called the ideal and nadir DMUs are constructed and used as reference points to evaluate a set of information technology (IT) investment strategies based on their Euclidean distance from these reference points. The best relative efficiency of the fuzzy ideal DMU and the worst relative efficiency of the fuzzy nadir DMU are determined and combined to rank the DMUs. A numerical example is presented to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures and algorithms.     

Cone ratio data envelopment analysis and multi-objective programming

A new ‘cone ratio’ data envelopment analysis (DEA) model that substantially generalizes the Charnes-Cooper-Rhodes (CCR) model and the Charnes-Cooper-Thrall approach characterizing its efficiency classes is developed and studied. It allows for infinitely many decision-making units (DM Us) and arbitrary closed convex cones for the virtual multipliers as well as the cone of positivily of the vectors involved. Generalizations of linear programming and polar cone equalizations arc the analytical vehicles employed.     

An interactive application of data envelopment analysis in microcomputers

This article describes a general-purpose microcomputer code for data envelopment analysis (DEA) that incorporates four different DEA models in the form of a user-friendly, menu-driven structure.Research financially supported by Dean's Professorship, College of Business, the Ohio State University.     

数据包络分析模型的化工试验设计方法评价

数据包络分析(DEA)是以“相对效率评价”基于化工试验中反应物、生成物之间的投入、产出关系,探讨了化工试验设计,主要探讨了在化工试验设计中DEA作为评价正交试验设计方法的一种有效的分析工具的理论和应用。实例分析表明,将DEA方法运用于化工试验设计的评价具有计算简单,意义清楚的特点,是对正交试验设计的有益补充。     

Multiobjective target setting in data envelopment analysis using AHP

In this paper two new target setting DEA approaches are proposed. The first one is an interactive multiobjective method that at each step of the process asks the decision maker (DM) which inputs and outputs he wishes to improve, which ones are allowed to worsen and which ones should stay at their current level. The local relative priorities of these inputs and outputs changes are computed using the analytic hierarchy process (AHP). After obtaining the candidate target, the DM can update his preferences for improving, worsening or maintaining current inputs and outputs levels and obtain a new candidate target. Thus continuing, until a satisfactory operating point is computed. The second method proposed uses a lexicographic multiobjective approach in which the DM specifies a priori a set of priority levels and, using AHP, the relative importance given to the improvements of the inputs and outputs at each priority level. This second approach requires solving a series of models in order, one model for each priority level. The models do not allow for worsening of neither inputs nor outputs. After the lowest priority model has been solved the corresponding target operating point is obtained. The application of the proposed approach to a port logistics problem is presented.     

Value of the stochastic efficiency in data envelopment analysis

This article examines the potential benefits of solving a stochastic DEA model over solving a deterministic DEA model. It demonstrates that wrong decisions could be made whenever a possible stochastic DEA problem is solved when the stochastic information is either unobserved or limited to a measure of central tendency. We propose two linear models: a semi-stochastic model where the inputs of the DMU of interest are treated as random while the inputs of the other DMUs are frozen at their expected values, and a stochastic model where the inputs of all of the DMUs are treated as random. These two models can be used with any empirical distribution in a Monte Carlo sampling approach. We also define the value of the stochastic efficiency (or semi-stochastic efficiency) and the expected value of the efficiency.     

Optimal profit-maximizing system design data envelopment analysis models

This research introduces a new type of data envelopment analysis (DEA) model termed the optimal system design (OSD) DEA model. Conventional DEA models evaluate DMUs’ performances given their known input and output data. The OSD DEA models take this one step further. They optimally design a DMU’s resource allocation in terms of profit maximization given the DMU’s total available budget. The need to design optimal systems is quite common and is sometimes necessary in practice. In actual fact, this study demonstrates that through the OSD DEA models, we can provide DMUs with more information than optimal portfolios of resources such as optimal budgets and budget congestion, i.e., the more the budget is consumed, the less the maximal profit. The proposed OSD DEA models are linear programs, and thus can be solved by the standard LP solvers to obtain DMUs’ optimal designs. However, to derive the DMUs’ corresponding optimal budgets, and to verify if the DMUs provide evidence of budget congestion, we need to modify the solvers, which may not be trivial. Therefore, this study exploits the special structures of the models to develop a simple solution method that can directly not only derive both a DMU’s optimal design and optimal budget, but can also check for the existence of budget congestion.     

An extended multiple criteria data envelopment analysis model

Several researchers have adapted the data envelopment analysis (DEA) models to deal with two inter-related problems: weak discriminating power and unrealistic weight distribution. The former problem arises as an application of DEA in the situations where decision-makers seek to reach a complete ranking of units, and the latter problem refers to the situations in which basic DEA model simply rates units 100% efficient on account of irrational input and/or output weights and insufficient number of degrees of freedom. Improving discrimination power and yielding more reasonable dispersion of input and output weights simultaneously remain a challenge for DEA and multiple criteria DEA (MCDEA) models. This paper puts emphasis on weight restrictions to boost discriminating power as well as to generate true weight dispersion of MCDEA when a priori information about the weights is not available. To this end, we modify a very recent MCDEA models in the literature by determining an optimum lower bound for input and output weights. The contribution of this paper is sevenfold: first, we show that a larger amount for the lower bound on weights often leads to improving discriminating power and reaching realistic weights in MCDEA models due to imposing more weight restrictions; second, the procedure for sensitivity analysis is designed to define stability for the weights of each evaluation criterion; third, we extend a weighted MCDEA model to three evaluation criteria based on the maximum lower bound for input and output weights; fourth, we develop a super-efficiency model for efficient units under the proposed MCDEA model in this paper; fifth, we extend an epsilon-based minsum BCC-DEA model to proceed our research objectives under variable returns to scale (VRS); sixth, we present a simulation study to statistically analyze weight dispersion and rankings between five different methods in terms of non-parametric tests; and seventh, we demonstrate the applicability of the proposed models with an application to European Union member countries.     

The upper and lower bound evaluation based on the quantile efficiency in stochastic data envelopment analysis

Data envelopment analysis (DEA) has been extended to handle random inputs and outputs by using chance constrained programming. In this paper, for DMUs with random inputs and outputs, we aim to measure a kind of relative efficiency, and achieve it from the optimistic viewpoint and the pessimistic viewpoint respectively. Considering the quantile of the distribution of the weighted output-input ratio of each DMU, we develop two stochastic DEA models to obtain the upper and lower bounds of the quantile efficiency under a constraint, and then achieve an interval efficiency evaluation. The best quantile efficiency and the worst quantile efficiency achieved by our models are closely similar to the CCR efficiency and belong to relative efficiencies. Further, the deterministic equivalents of our models are developed when the input and output vector of each DMU follows a multivariate joint normal distribution. Finally, three examples are presented to illustrate the performance of our approach.     

Fuzzy data envelopment analysis: A discrete approach

Data envelopment analysis (DEA) as introduced by Charnes, Cooper, and Rhodes (1978) is a linear programming technique that has widely been used to evaluate the relative efficiency of a set of homogenous decision making units (DMUs). In many real applications, the input-output variables cannot be precisely measured. This is particularly important in assessing efficiency of DMUs using DEA, since the efficiency score of inefficient DMUs are very sensitive to possible data errors. Hence, several approaches have been proposed to deal with imprecise data. Perhaps the most popular fuzzy DEA model is based on α-cut. One drawback of the α-cut approach is that it cannot include all information about uncertainty. This paper aims to introduce an alternative linear programming model that can include some uncertainty information from the intervals within the α-cut approach. We introduce the concept of “local α-level” to develop a multi-objective linear programming to measure the efficiency of DMUs under uncertainty. An example is given to illustrate the use of this method.     

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.     

Evaluating ecommerce websites cognitive efficiency: An integrative framework based on data envelopment analysis

This paper presents an integrative framework to evaluate ecommerce website efficiency from the user viewpoint using Data Envelopment Analysis (DEA). This framework is inspired by concepts driven from theories of information processing and cognition and considers the website efficiency as a measure of its quality and performance. When the users interact with the website interfaces to perform a task, they are involved in a cognitive effort, sustaining a cognitive cost to search, interpret and process information, and experiencing either a sense of satisfaction or dissatisfaction for that. The amount of ambiguity and uncertainty, and the search (over-)time during navigation that they perceive determine the effort size – and, as a consequence, the cognitive cost amount – they have to bear to perform their task. On the contrary, task performing and result achievement provide the users with cognitive benefits, making interaction with the website potentially attractive, satisfying, and useful. In total, 9 variables are measured, classified in a set of 3 website macro-dimensions (user experience, site navigability and structure). The framework is implemented to compare 52 ecommerce websites that sell products in the information technology and media market. A stepwise regression is performed to assess the influence of cognitive costs and benefits that mostly affect website efficiency.     

Alternative solutions for classifying inputs and outputs in data envelopment analysis

In conventional data envelopment analysis (DEA) models, a performance measure whether as an input or output usually has to be known. Nevertheless, in some cases, the type of a performance measure is not clear and some models are introduced to accommodate such flexible measures. In this paper, it is shown that alternative optimal solutions of these models has to be considered to deal with the flexible measures, otherwise incorrect results might occur. Practically, the efficiency scores of a DMU could be equal when the flexible measure is considered either as input or output. These cases are introduced and referred as share cases in this study specifically. It is duplicated that share cases must not be taken into account for classifying inputs and outputs. A new mixed integer linear programming (MILP) model is proposed to overcome the problem of not considering the alternative optimal solutions of classifier models. Finally, the applicability of the proposed model is illustrated by a real data set.     

Fuzzy data envelopment analysis and its application to location problems

In this paper, fuzzy DEA (data envelopment analysis) models are proposed for evaluating the efficiencies of objects with fuzzy input and output data. The obtained efficiencies are also fuzzy numbers that reflect the inherent ambiguity in evaluation problems under uncertainty. An aggregation model for integrating fuzzy attribute values is provided in order to rank objects objectively. Using the proposed method, a case study involving a restaurant location problem is analyzed in detail. Rent of establishment, traffic amount, level of security, consumer consumption level and competition level are identified as the primary factors in determining an ideal location for a Japanese-style rotisserie restaurant. Based on field investigation, the uncertain information on primary factors is represented by fuzzy numbers. Using the fuzzy aggregation model, the best location of restaurant is determined. The case study shows that fuzzy DEA models can be quite useful for solving business problems under uncertainty.