Benchmarking and Target Setting in Weight Restriction Context

In models of data envelopment analysis (DEA), an optimal set of input and output weights is generally assumed to represent the assessed decision making unit (DMU) in the best light in comparison to all the other DMUs. The paper shows that this may not be correct if absolute weight bounds or some other weight restrictions are added to the model. A consequence may be that the model will underestimate the relative efficiency of DMUs. The incorporation of weight restrictions in a maximin DEA model is suggested. This model can be further converted to more operational forms, which are similar to the classical DEA models.

This study aims to explore whether a machine learning algorithm can be used to make improvements in assessing unit efficiencies via a data envelopment analysis (DEA) model. In this study, a DEA model is used to calculate the efficiency scores of Desicion Making Units (DMUs). Then, an ML algorithm is trained that aims to predict the single output using inputs. Ranking of input features based on relative feature importance values obtained from the trained ML model is fed to the DEA model as weight restrictions. As a result, the two DEA models are compared with each other. ML-based insights (feature importance ranking) improve the DEA model in the direction of fewer zero weights. The additional weight restrictions are data depdendent, and hence realistic. As a novel approach, this study proposes the use of machine learning-based feature importance values to overcome a limitation of a DEA model.

The appreciative democratic voice of DEA: A case of faculty academic performance evaluation

Efficiency measurement is crucial to management for performance evaluation of several decision-making units (DMUs) in order to find the most efficient unit. Data envelopment analysis (DEA) is a practical and popular method that has been used widely for efficiency measurement in many applications. Thus, in the literature of DEA, several mixed integer DEA models are developed to efficiency measure and find the best efficient unit. In some situations, some factors named dual-role factors may be simultaneously considered as both inputs and outputs. However, a little attention has been paid in the literature of DEA to these types of factors. The current paper develops a new mixed integer linear DEA model to identify the best efficient DMU in the presence of dual-role factors. The basic DEA models consider different roles for each dual-role factor, and also solve at least one model for each DMU to determine the best unit. However, the developed approach in this paper considers a unique role for each dual-role factor, and also determines the best unit through by solving just one mixed integer DEA model. Two numerical examples are used to illustrate the profits and applicability of the developed approach.

Cross-efficiency aggregation in DEA models using the evidential-reasoning approach

Data envelopment analysis (DEA) is a non-parametric technique for measuring the efficiency of decision making units (DMU) with exact input and output terms. So far, a number of DEA models with interval data have been developed. The radial DEA model such as CCR or BCC model with interval data are well known as basic DEA models with interval data. However, these radial DEA models have some defects. In this study, we develop a new approach based upon the slacks-based measurement (SBM) of super-efficiency model for dealing with interval data in DEA. The SBM super-efficiency DEA model can not only discriminate the performance of efficient DMUs from inefficient ones, but can distinguish between the efficient DMUs. In addition, this model can overcome the drawback that the super-efficiency model can be infeasible under variable returns to scale (VRS) assumption. An illustrative example is provided to verify the idea of this paper and show its potential application and validity.

A generalized model for data envelopment analysis with interval data

DEA model with shared resources and efficiency decomposition

Weextend the concept of returns to scale in Data Envelopment Analysis(DEA) to the weight restriction environments. By the additionof weight restrictions, the status of returns to scale, i.e., increasing, constant and decreasing may suffer a change. Wefirst define ``returns to scale'' under weight restrictions andpropose a method for identifying the status of returns to scale.Then, it is demonstrated that the region of the most productivescale size (MPSS) will usually be narrowed by this addition.For an inefficient decision making unit (DMU), a simple rulefor determining the status of returns to scale of its projectedDMU will be presented. An empirical study compares the resultsof the proposed method with those of the BCC model and demonstratesthe change in the MPSS for both models.

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.

Park proposed a pair of mathematical data envelopment analysis (DEA) models to estimate the lower and upper bound of efficiency scores in the presence of imprecise data. This article illustrates that his approach suffers from some drawbacks: (i) it may convert weak ordinal data into an incorrect set of precise data; (ii) it utilizes various production frontiers to obtain an interval efficiency score for each decision making unit (DMU); (iii) in the absence of exact output data (pure ordinal output data), the approach leads to a meaningless model; (iv) the built model is infeasible with pure ordinal input data; (v) it may include free or unlimited production output which results in unreliable and suspicious results. Moreover, the utilized models by Park involve a positive lower bound (non-Archimedean epsilon) for the weights to deter them from being zero. However, the author ignored the requirement of determining a suitable value for the epsilon. This study constructs two new DEA models with a fixed and unified production frontier (the same constraint set) to compute the upper and lower bounds of efficiency. It is demonstrated that the suggested models can successfully capture the aforementioned shortcomings. Although these models are also epsilon-based, a new model is developed to obtain a suitable epsilon value for the proposed models. It is proved that the suggested approach effectively eliminates all the weaknesses. Additionally, a case study of Iranian Space Agency (ISA) industry is taken as an example to illustrate the superiority of the new approach over the previous ones.

The main goal of this paper is to develop a new data envelopment analysis (DEA) model to use optimal weights of each decision making unit (DMU) to improve its relative efficiency aligned with other DMUs. In spite of the vast amount of studies in this area and related tools and techniques, current literature deploys the optimal weights of DMUs to calculate the DMUs' relative efficiency and benchmarking for each DMU is less investigated. In order to fill this gap, this paper proposes a model for obtaining benchmark(s) for each DMU. Furthermore, a numerical example is used to illustrate the capability of the proposed model.

In this paper, we have formulated Data Envelopment Analysis (DEA) models to reduce the inputs in an inefficient Decision Making Unit (DMU) when the specific inputs are under the constant sum constraint. We have also extended the models to reallocate the excess input without any reduction in efficiency of other DMUs. These DEA models and methods developed in this work will help decision makers in developing an optimal strategy to transfer excess input to other DMUs. Theoretical results have been illustrated with the help of a case study.

Data envelopment analysis (DEA) is a method for measuring efficiency of peer decision-making units (DMUs). Conventional DEA evaluates the performance of each DMU using a set of most favourable weights. As a result, traditional DEA models can be considered methods for the analysis of the best relative efficiency or analysis of the optimistic efficiency. DEA efficient DMUs obtained from conventional DEA models create an efficient production frontier. Traditional DEA can be used to identify units with good performance in the most desirable scenarios. There is a similar approach that evaluates the performance indicators of each DMU using a set of most unfavourable weights. Accordingly, such models can be considered models for analysing the worst relative efficiency or pessimistic efficiency. This approach uses the inefficient production frontier for determining the worst relative efficiency that can be assigned to each DMU. DMUs lying on the inefficient production frontier are referred to as DEA inefficient while those neither on the efficient frontier nor on the inefficient frontier are declared DEA inefficient. It can be argued that both relative efficiencies should be considered simultaneously and any approach with only one of them would be biased. This paper proposed the integration of both efficiencies as an interval so that the overall performance score would belong to this interval. It was shown that efficiency interval provided more information than either of the two efficiencies, which was illustrated using two numerical examples.

Greenhouse gas (GHG) is a main cause for climate anomalies, and thus, declining GHG emissions becomes an essential task for enterprises, especially for international liner shipping companies, to achieve the goal of corporate social responsibility (CSR). To liner shipping companies, main emitting gases are CO2, SOx, and NOx that cause marine pollution and global warming. To decline environmental warming and marine pollution, efficiency measure about GHG emissions for liner shipping companies is important. Due to data specifications of GHG, slack-based measure (SBM) data envelopment analysis (DEA) and super SBM DEA models focus on undesirable outputs are proposed and integrated into new DEA models. Through these models above, GHG emissions of liner shipping companies for varied years viewed as peer decision-making units (DMUs) are measured. Then, relative efficient DMUs are useful references for GHG emissions of liner shipping companies in emitting policies and technologies to reduce marine pollution.