In the determination of the most efficient decision making unit in data envelopment analysis

In recent years, several mixed integer linear programming (MILP) models have been proposed for determining the most efficient decision making unit (DMU) in data envelopment analysis. However, most of these models do not determine the most efficient DMU directly; instead, they make use of other less related objectives. This paper introduces a new MILP model that has an objective similar to that of the super-efficiency model. Unlike previous models, the new model’s objective is to directly discover the most efficient DMU. Similar to the super-efficiency model, the aim is to choose the most efficient DMU. However, unlike the super-efficiency model, which requires the solution of a linear programming problem for each DMU, the new model requires that only a single MILP problem be solved. Consequently, additional terms in the objective function and more constraints can be easily added to the new model. For example, decision makers can more easily incorporate a secondary objective such as adherence to a publicly stated preference or add assurance region constraints when determining the most efficient DMU. Furthermore, the proposed model is more accurate than two recently proposed models, as shown in two computational examples.     

Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis

A mixed integer linear model for selecting the best decision making unit (DMU) in data envelopment analysis (DEA) has recently been proposed by Foroughi [Foroughi, A. A. (2011a). A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers and Industrial Engineering, 60(4), 550–554], which involves many unnecessary constraints and requires specifying an assurance region (AR) for input weights and output weights, respectively. Its selection of the best DMU is easy to be affected by outliers and may sometimes be incorrect. To avoid these drawbacks, this paper proposes three alternative mixed integer linear programming (MILP) models for identifying the most efficient DMU under different returns to scales, which contain only essential constraints and decision variables and are much simpler and more succinct than Foroughi’s. The proposed alternative MILP models can make full use of input and output information without the need of specifying any assurance regions for input and output weights to avoid zero weights, can make correct selections without being affected by outliers, and are of significant importance to the decision makers whose concerns are not DMU ranking, but the correct selection of the most efficient DMU. The potential applications of the proposed alternative MILP models and their effectiveness are illustrated with four numerical examples.     

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.     

A new data envelopment analysis method for ranking decision making units: an application in industrial parks

Relative efficiency of decision‐making units (DMUs) is assessed by classical data envelopment analysis (DEA) models. DEA is a popular technique for efficiency evaluation. There might be a couple of efficient DMUs. Classical DEA models cannot fully rank efficient DMUs. In this paper, a novel technique for fully ranking all DMUs based on changing reference set using a single virtual inefficient DMU is proposed. To this end, the first concept of virtual DMU is defined as average of all inefficient DMUs. Virtual DMU is a proxy of all inefficient DMUs. This new method proposes a new ranking method that takes into account impact of efficient DMUs on virtual DMU and impact of efficient DMUs on influences of other efficient DMUs. A case study is given to show applicability of the proposed approach.     

A new mixed integer linear model for selecting the best decision making units in data envelopment analysis

In a recent paper by Amin (Amin, Gholam R. (2009). Comment on finding the most efficient DMUs in DEA: An improved integrated model. Computers & Industrial Engineering, 56, 1701–1702), he proposed an improved approach to determine a single efficient DMU as the most (or the best) efficient DMU. It will be shown that this nonlinear mixed integer model may fail to produce a solution since it can be infeasible in some cases. In this paper, a linear mixed integer model is proposed which is feasible and can produce a single efficient DMU as well. The model can also be extended to rank all extreme efficient DMUs. Some properties and advantages of the model will be explained. The contents of the paper will be illustrated by some numerical examples including a real data set of nineteen facility layout alternatives.     

Negative data in data envelopment analysis: Efficiency analysis and estimating returns to scale

The classic Data Envelopment Analysis (DEA) models developed with the assumption that all inputs and outputs are non-negative, whereas, we may face a case with negative data in the actual business world. So, the need to adapt the DEA models so that they are applicable to cases includes inputs and outputs which can take both negative and non-negative values has been an issue. It can be readily demonstrated that the assumption of constant returns to scale (CRS) is not possible in technologies under negative data. So, one of the interesting and challenge questions is how to determine the state of RTS in the presence of negative data under variable returns to scale (VRS) technology. Accordingly, in this contribution, we first address the efficiency measure and then suggest a method to discover the state of returns to scale (RTS) in the presence of negative input and output values which has not been discussed much enough so far in DEA literature. Finally, the main results are elaborated by some illustrative examples.     

Comments on finding the most efficient DMUs in DEA: An improved integrated model

This paper improves the integrated DEA model proposed for finding the most efficient DMUs introduced by Amin and Toloo, [Amin, Gholam R., Toloo, M. (2007). Finding the most efficient DMUs in DEA: An improved integrated model. Computers & Industrial Engineering, 52(2), 71–77]. The paper shows the problem of using the integrated DEA model and presents an improved integrated DEA model for determining a single efficient unit. Also the paper indicates the property of the improvements mathematically and a numerical example shows the usefulness and intelligibility of the study.     

An enumeration algorithm for integer‐valued data envelopment analysis

Data envelopment analysis (DEA) models assume real‐valued inputs and outputs, but on many occasions, some inputs and/or outputs can only take integer values. In these cases, using DEA models can result in misleading efficiency assessments and inaccurate performance targets. In this paper, we propose an enumeration algorithm for computing efficiency scores and performance targets of decision‐making units with integer value inputs/outputs. In the presented algorithm, we do not use any of the mixed integer linear programming (MILP) models that are used in previous studies. We show that the result of our algorithm and that of the MILP model presented in this context is the same. We also generalize our algorithm for different types of returns to scale as well as for the hybrid setting with real‐valued data.     

Right and left returns to scales in data envelopment analysis: Determining type and measuring value

This study identifies types and values of right and left returns to scales (RTSs) of efficient decision making units (DMUs) in data envelopment analysis (DEA). In this research, we first introduce a new approach to estimate types of right and left returns to scales of efficient DMUs and then, values of right and left returns to scales of these DMUs are measured by presenting two new DEA models.     

Estimating most productive scale size with imprecise-chance constrained input–output orientation model in data envelopment analysis

Varieties of data envelopment analysis (DEA) models have been formulated to assess performance of decision making units (DMUs) in various fields with different data such as: deterministic, interval, fuzzy, etc. Classic DEA requires that values of all inputs and outputs are known exactly. However, this assumption may not be true, since in practice, data can not be precisely measured. Furthermore, a realistic situation is no longer realistic when imprecise and uncertain information are neglected to analyze efficiency of DMUs and measurement errors and data entry errors, etc.     

A strategic model for supply chain design with logical constraints: formulation and solution

This paper proposes a strategic production–distribution model for supply chain design with consideration of bills of materials (BOM). Logical constraints are used to represent BOM and the associated relationships among the main entities of a supply chain such as suppliers, producers, and distribution centers. We show how these relationships are formulated as logical constraints in a mixed integer programming (MIP) model, thus capturing the role of BOM in the selection of suppliers in the strategic design of a supply chain. A test problem is presented to illustrate the effectiveness of the formulation and solution strategy. The results and their managerial implications are discussed.Scope and purposeSupply chain design is to provide an optimal platform for efficient and effective supply chain management. The problem is often an important and strategic operations management problem in supply chain management. This paper shows how the mixed integer programming modeling techniques can be applied to supply chain design problem, where some complicated relations, such as bills of materials, are involved. We discuss how to solve such a complicated model efficiently.     

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.     

Farming system performance and water use efficiency in the Tunisian semi‐arid region: data envelopment analysis approach

Understanding farming strategies and identifying the parameters controlling production technologies are the fundamental elements required to modify the consumption of the irrigated sector without compromising production objectives. In this regard, the objective of this investigation is to analyse the performance of irrigated farms in the region of Sidi Bouzid, Tunisia. Firstly, farm surveys were carried out in both public and private irrigated areas. Secondly, an analysis of the production system within these farms showed an appropriate technology process. Moreover, the application of the data envelopment analysis approach allowed the measurement of technical and allocative efficiency. The comparison between both production systems, based on public and private resources, revealed that more important resources were wasted under the private than under the public water management system. Thus, the surface wells creation strategy, as a second resource for irrigation, was found to be against the sustainable use of an already overexploited groundwater. However, such strategy is justified when analysing allocative efficiency scores. Indeed, the profitability of the activity, based on the use of wells for irrigation, appears to be much higher than the one based on public resources.     

A flexible ANN-GA-multivariate algorithm for assessment and optimization of machinery productivity in complex production units

This paper presents a flexible algorithm based on artificial neural networks (ANNs), genetic algorithms (GAs), and multivariate analysis for performance assessment and optimization of complex production units (CPUs) with respect to machinery productivity indicators (MPIs). Multivariate techniques include data envelopment analysis (DEA), principal component analysis (PCA) and numerical taxonomy (NT). Two case studies are considered to show the applicability of the proposed approach. In the first case, the machinery productivity indicators are categorized into four standard classes as availability, machinery stoppage, random failure and value added and production value. In the second case, the productivity of production units in terms of health, safety, environment and ergonomics indicators is evaluated. The flexible algorithm is capable of handling both linearity and complexity of data sets. Moreover, ANN and GA are efficiently applied to cover nonlinearity and complexity of CPUs. The results are also validated and verified by the internal mechanism of the algorithm. The algorithm is applied to a large set of production units to show its superiority and applicability over conventional approaches. Results show that, in the case of having non-linear data sets, ANN outperforms GA and conventional approaches. The flexible algorithm of this study may be easily extended to other units for assessment and optimization of CPUs with respect to machinery indicators.     

基于逆数据包络分析法的中医方药评价与药量计算研究

针对中医组方的药量推算建模问题,提出了基于证候上下文分析的逆数据包络分析（IDEA）算法。该算法以证侯的典型方剂为依据,以数据包络分析为评价工具,建立起反映证候演化的方药评价模型;依据代表证候状态的评价值,给相应的证型症状信息赋值,以完成“词计算”过程。最后,把具体的辨证过程植入到证侯发展的上下文环境中,以典型证型的“词计算”为依据,给出具体案例的证侯状态评价,再采用IDEA算法推算出药量数据。该模型的推算结果表明,它能够反映中医的一般用药规律,这将对辨证论治组方环节的数值化、客观化研究提供一种可能的思路。     

A new fuzzy DEA model for evaluation of efficiency and effectiveness of suppliers in sustainable supply chain management context

Sustainable supply chain management (SSCM) has received much consideration from corporate and academic over the past decade. Sustainable supplier performance evaluation and selection plays a significant role in establishing an effective SSCM. One of the techniques that can be used for sustainable supplier performance evaluation and selection is data envelopment analysis (DEA). In real world problems, the inputs and outputs might be imprecise. This paper develops an integrated DEA enhanced Russell measure (ERM) model in fuzzy context to select the best sustainable suppliers. A case study is presented to exhibit the efficacy of the proposed method for sustainable supplier selection problem in a resin production company. The case study demonstrates that the proposed model can measure effectiveness, efficiency, and productivity in uncertain environment with different α levels. Also, it shows that the proposed model aids decision makers to deal with economic, social, and environmental factors when selecting sustainable suppliers.     

Pareto–Koopmans efficiency in two‐stage network data envelopment analysis in the presence of undesirable intermediate products and nondiscretionary factors

Many studies have recently been conducted on the evaluation of system performance with a two‐stage network structure in data envelopment analysis (DEA) literature. One of the topics of interest to researchers has been the mitigation of undesirable products or nondiscretionary factors into their corresponding possible production set (PPS) and their impact on overall efficiency calculations. Determination of decision‐making units (DMUs) with Pareto–Koopmans efficiency status is decisive in identifying benchmark units. The calculated overall efficiency status is compromised when both undesirable products and nondiscretionary factors are present. This work utilizes an axiomatic approach. A novel PPS for a two‐stage network in presence of undesirable intermediate products and nondiscretionary exogenous inputs is introduced. Based on this PPS and by focusing on the principle of mathematical dominance, new models for evaluating overall and divisional efficiencies are presented. In addition, by proposing a two‐step network DEA approach, a necessary and sufficient condition for detection of DMUs with Pareto–Koopmans efficiency status is provided. And by introducing a two‐step algorithm, a novel technique for determining overall efficiency conditions is produced. Finally, the proposed technology is applied to a practical example, and outcomes are discussed.