A New Stochastic Model for Classifying Flexible Measures in Data Envelopment Analysis

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.

Data envelopment analysis (DEA) allows evaluation of the relative efficiencies of similar entities, known as decision making units (DMUs), which consume the same types of resources and offer similar types of products. It is known that under certain circumstances, when the number of DMUs does not meet the DEA Golden Rule, that is, this number is not sufficiently large compared to the total number of inputs and outputs, traditional DEA models often yield solutions that identify too many DMUs as efficient. In fact, this weak discrimination power and unrealistic weight distribution presented by DEA models remain a major challenge, leading to the development of models to improve this performance, such as: multiple criteria data envelopment analysis (MCDEA), bi-objective multiple criteria data envelopment analysis, goal programming approaches to solve weighted goal programming (WGP–MCDEA) and extended–MCDEA. This paper proposes a new MCDEA model which is based on goal programming, with and without super efficiency concepts, and presents test results that show its advantages over the above cited models. A set of problems from the literature and real-world applications are used in these tests. The results show that the new MCDEA model provides better discrimination of DMUs in all tested problems, and provides a weight dispersion that is statistically equal to that obtained by other MCDEA models. An additional feature of the proposed model is that it allows the identification of the input and output variables that are most important to the problem, to make it easier for the decision maker to improve the efficiency of the DMUs involved. This is very useful in practice, because in general, the available resources are scarce, so it is a further advantage of the proposed MCDEA model over the others tested.

When the number of Decision-Making Units (DMUs) is not large enough compared to the total number of input parameters and outputs, traditional Data Envelopment Analysis (DEA) and Network Data Envelopment Analysis (NDEA) models often produce solutions that identify many DMUs as efficient, in addition to obtaining unrealistic weight distributions. In fact, this poor discrimination power and unrealistic weight distribution presented by DEA and NDEA models remain a major challenge, leading to the development of models to improve this performance. Thus, this paper proposes a Multiple Criteria Network Data Envelopment Analysis (MCNDEA), based on relational NDEA models. The idea of this model is to be used in network structures. To test the MCNDEA model, one a real instance linked to an evaluation problem of academic departments of a public university was used. Other instances were also used to validate the proposed MCNDEA, and these tests are included in the supplementary files. Finally, it should be noted that, in summary, the model proposed in this article had greater discrimination power of the analyzed DMUs, being able to identify the most efficient departments in each of the considered stages, besides pointing out to the University Management points of improvement regarding the best use of its resources for each department.

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

Globally, insurance and takaful companies play a crucial role in economic and financial development of a country. Malaysia’s insurance sector has undergone substantial changes compared to two decades ago. Due to intense competition observed in Malaysian insurance industry, efficiency measurement and a complete efficiency ranking of insurance companies are very important for the decision makers so that necessary changes and improvement can be made. Data Envelopment Analysis (DEA) is a non-parametric method that has been acknowledged as an effective method to measure the efficiency of homogeneous decision-making units (DMUs). The main advantage of DEA is its ability to handle multiple inputs and outputs. However, standard DEA has poor discrimination power since it generates too many efficient units especially when the number of DMUs under study is insufficient in comparison to number of inputs and outputs. It cannot discriminate efficient units and therefore unable to give a complete ranking of DMUs. This study aimed to overcome the ranking problem found in standard DEA by integrating DEA and Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) II. The hybrid method was applied to evaluate the efficiency and ranking of 22 life insurance and takaful companies in Malaysia from the period of 2017 to 2018. Input variables used in this study comprised of fees and commission, and management expenses. Meanwhile, output variables were net premium and generated investment income. The proposed method involved two stages. In the first stage, DEA was applied to obtain the efficient scores for the DMUs. In the second stage, PROMETHEE II was implemented to rank the efficient units. This hybrid method has successfully obtained full ranking of all the insurance companies under study. The inefficient companies can learn strategies and practices from efficient companies to enhance their services. It is recommended for future research to integrate DEA with other Multi Criteria Decision Making (MCDM) methods such as TOPSIS and VIKOR to fully rank the DMUs.

Data envelopment analysis (DEA) is a tool for measuring the relative efficiency of decision-making units (DMUs) that perform similar tasks. One of the uses of the DEA is the establishment of benchmarks for inefficient DMUs. These benchmarks play the role of target for inefficient DMUs. However, traditional DEA (TDEA) models fail to rank the efficient DMUs, and as a result, they cannot determine a benchmark for the inefficient DMUs. To overcome this shortcoming, this paper proposes virtual network DEA (NDEA) approach. The proposed method not only ranks the whole inefficient and efficient DMUs but also establishes a virtual benchmark called ideal DMU. The case study demonstrates the applicability of the proposed model.

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.

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

Variable selection is an important step in data envelopment analysis (DEA) when the number of decision making units (DMUs) is insufficient. This research thus proposes a two-stage variable selection method integrating a well-known supervised machine learning technique, the random forest algorithm. In the first stage, a baseline DEA model with full input and output variables is implemented and each DMU can be determined as being efficient or inefficient. In the second stage, a random forest is trained to learn how to classify efficient or inefficient DMUs well in high dimensions. Accordingly, the importance of each variable can be calculated based on permutation importance indices in random forest. This paper further discusses two issues about data augmentation in order to improve the robustness of permutation importance when the number of DMUs is quite small.

The present study seeks to investigate efficiency of roads in provinces in Iran. Considering the resource limitation, prioritisation of roads seems necessary for better allocation of resources. Since it is possible to investigate decision-making units (DMUs) where there are several inputs and outputs without considering any weight for them in data envelopment analysis, this method is very suitable for ranking. In order to analyse efficiency, BCC model with variable return to scale was used and given that a number of DMUs become efficient after solving the model, Anderson-Peterson method was employed to determine strong efficiency. Considering that one of the advantages of data envelopment analysis is the possibility of offering a progress model for inefficient DMUs, the essential changes in inputs and outputs of inefficient DMUs for being efficient have been mentioned.

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.

Strategic alliances and partnerships based on the semi-additive production technology in DEA

Efficiency evaluation of homogenous decision making units (DMUs), is one of the primary objectives of data envelopment analysis (DEA), in which the large number of inputs or outputs compared with the number of DMUs leads to decreased evaluation precision of DEA models. Overcoming this problem is the main issue in two-level DEA. In the present study, we use the multi objective linear programming (MOLP) method proposed by Sumpsi et al., which is based on constructing the pay-off matrix and using goal programming (GP), to investigate this problem. Furthermore, we discuss the enhanced Russell's model for evaluating and benchmarking DMUs with two-level inputs and outputs. The proposed method is applied to 24 branches of an Iranian commercial bank.

Data Envelopment Analysis (DEA) is a popular non-parametric technique for the assessment of efficiency of a set of homogeneous decision making units (DMUs) with the same set of inputs and outputs. In the conventional DEA models, it is assumed that all variables are fully controllable. However, in the real-world applications of DEA, some of the variables are completely uncontrollable or partially controllable. In this paper, we are concerned about partially controllable variables which are called semi-discretionary variables. In DEA models, in the presence of semi-discretionary variables, decision makers have partial control on these variables and the proportional changes are possible to some extent. Previous DEA models with semi-discretionary variables consider a certain level of control on the variables which is fixed and it is given by decision makers or a higher authority. Since this level is usually given by experts, it is possible that in some cases all experts may not come up with an agreement, so in this paper we consider variable instead of fixed level of control on each semi-discretionary variable. In the presence of semi-discretionary variables, the proportional changes in inputs and out-puts may not be feasible and as a result the obtained target value by conventional DEA models is not achievable for an inefficient DMU. Thus, we propose a bi-objective model to evaluate DMUs when modifying a variable to its target value should be managed by decision makers in a voting system. One of the advantages of the proposed model is including decision making conditions directly into a DEA model.

Data Envelopment Analysis (DEA) models with weight restrictions (WRs) have proven valuable for benchmarking and target setting. Although the DEA literature has explored the incorporation of managerial preferences and value judgments regarding the relative worth of inputs and outputs, as well as the establishment of targets in benchmarking contexts, little attention has been devoted to target setting under restricted DEA models. Moreover, despite the significant advances offered by minimum distance models for target establishment, limited research has addressed benchmarking improvement plans that integrate expert opinions and prior knowledge. Some studies have examined minimum distance models constrained to the efficient Assurance Region (AR) frontier, primarily by extending the concept of closest targets under WR. In contrast, this paper develops improvement plans that deviate minimally from the closest target projection obtained from the original, unrestricted DEA model—termed the reference target. This reference target is considered an acceptable “peer” since it requires the least effort for a decision making unit (DMU) to reach optimal performance before incorporating WR. To this end, we developed a mixed-integer linear programming (MILP) model under the assumption of Variable Returns to Scale in DEA. The proposed approach is illustrated through an application to benchmarking the tourism performance of localities in Córdoba, Argentina. The results reveal realistic and achievable improvement plans for the analyzed localities, ensuring that both global efforts are managed and expert-imposed restrictions are satisfied.