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The traditional data envelopment analysis (DEA) model as a non-parametric technique can measure the relative efficiencies of a decision-making units (DMUs) set with exact values of inputs and outputs, but it cannot handle the imprecise data. The purpose of this paper is to establish a super efficiency interval data envelopment analysis (IDEA) model, an IDEA model based on cross-evaluation and a cross evaluation-based measure of super efficiency IDEA model. And the authors apply the proposed approach to data on the 29 public secondary schools in Greece, and further demonstrate the feasibility of the proposed approach.

In this paper, based on the IDEA model, the authors propose an improved version of establishing a super efficiency IDEA model, an IDEA model based on cross-evaluation, and then present a cross evaluation-based measure of super efficiency IDEA model by combining the super efficiency method with cross-evaluation. The proposed model cannot only discriminate the performance of efficient DMUs from inefficient ones, but also can distinguish between the efficient DMUs. By using the proposed approach, the overall performance of all DMUs with interval data can be fully ranked.

A numerical example is presented to illustrate the application of the proposed methodology. The result shows that the proposed approach is an effective and practical method to measure the efficiency of the DMUs with imprecise data.

The proposed model can avoid the fact that the original DEA model can only distinguish the performance of efficient DMUs from inefficient ones, but cannot discriminate between the efficient DMUs.

This paper introduces the effective method to obtain the complete rank of all DMUs with interval data.

The purpose of this paper is to solve the DEA model with grey interval data while the inputs/outputs have large interval length.

Some methods have been developed to calculate the interval efficiencies of the decision‐making unit (DMU) in DEA model with interval data, in which there are two shortcomings. One is that the evaluated DMU and referenced DMUs are not be dealt with fairly, as they are not counterparts in locations of inputs and outputs within possible ranges. Another is that efficiency intervals may be too wide to provide valuable information. This paper proposes the hypotheses of data consistency in DEA model. Under the hypotheses, linear programming (LP) models to solve the upper and lower bounds of interval efficiencies are established.

It is found that lengths of efficiency intervals under the hypotheses are shorter, which produces more reliable and informative evaluation results and DMUs are dealt with more fairly.

The method proposed in the paper could be used in efficiencies evaluation of enterprises, governments, etc. when the classic methods are invalid for the high uncertainty evaluation results.

The paper succeeds in proposing the hypotheses of data consistency and solving the DEA model with interval grey data under that.

Assessing inputs and outputs is a significant aspect of taking decisions while there are complex and multistage processes in many examinations. Due to the presence of interval performance measures in various real-world studies, the purpose of this study is to address the changes of interval inputs of two-stage processes for the perturbations of interval outputs of two-stage systems, given that the overall efficiency scores are maintained.

Actually, an interval inverse two-stage data envelopment analysis (DEA) model is proposed to plan resources. To illustrate, an interval two-stage network DEA model with external interval inputs and outputs and also its inverse problem are suggested to estimate the upper and lower bounds of the entire efficiency and the stages efficiency along with the variations of interval inputs.

An example from the literature and a real case study of the banking industry are applied to demonstrate the introduced approach. The results show the proposed approach is suitable to estimate the resources of two-stage systems when interval measures are presented.

To the best of the authors’ knowledge, there is no study to estimate the fluctuation of imprecise inputs related to network structures for the changes of imprecise outputs while the interval efficiency of network processes is maintained. Accordingly, this paper considers the resource planning problem when there are imprecise and interval measures in two-stage networks.

The purpose of this paper is to assess whether the relative efficiency of South African municipalities in primary health care and hospital care is different and whether South African municipalities can learn from each other to improve on their efficiency.

The paper employs efficiency scores, estimated with data envelopment analysis using data from the District Health Barometer of the Health Systems Trust to rank South African municipalities across primary health care and hospital health care.

The finding is that the ranking of municipalities is not the same across both types of health care when efficiency scores and efficiency score growth are contemplated. These results imply that municipalities in South Africa are generally inefficient, but with the possibility of learning from each other’s practice in order to increase their technical efficiency.

The health system authority should monitor service-specific best practices among municipalities so that they can use them as practice guidelines for other municipalities.

Previous studies in South Africa have not dis-aggregated efficiency analysis across municipalities which are health system components of the broader national health system.

Evaluating the performance of supply chains is a convoluted task because of the complexity that is inextricably linked to the structure of the aforesaid chains. Therefore, the purpose of this paper is to present an integrated approach for evaluating and sizing real-life health-care supply chains in the presence of interval data.

To achieve the objective, this paper illustrates an approach called Latin hypercube sampling by replacement (LHSR) to identify a set of precise data from the interval data; then the standard data envelopment analysis (DEA) models can be used to assess the relative efficiencies of the supply chains under evaluation. A certain level of data aggregation is suggested to improve the discriminatory power of the DEA models and an experimental design is conducted to size the supply chains under assessment.

The newly developed integrated methodology assists the decision-makers (DMs) in comparing their real-life supply chains against peers and sizing their resources to achieve a certain level of production.

The proposed integrated DEA-based approach has been successfully implemented to suggest an appropriate structure to the actual public pharmaceutical supply chain in Morocco.

The originality of the proposed approach comes from the development of an integrated methodology to evaluate and size real-life health-care supply chains while taking into account interval data. This developed integrated technique certainly adds value to the health-care DMs for modelling their supply chains in today's world.

Assessing the performance of medical laboratories plays an important role in the quality of health services. However, because of imprecise data, reliable results from laboratory performance cannot be obtained easily. The purpose of this paper is to illustrate the use of interval network data envelopment analysis (INDEA) based on sustainable development indicators under uncertainty.

In this study, each medical diagnostic laboratory is considered as a decision-making unit (DMU) and an INDEA model is used for calculating the efficiency of each medical diagnostic laboratory under imprecise inputs and outputs. The proposed model helps provide managers with effective performance scores for deficiencies and business improvements. The proposed model with realistic efficiency scores can help administrators manage their deficiencies and ultimately improve their business.

The results indicate that uncertainty can lead to changes in performance scores, rankings and performance classifications. Therefore, the use of DEA models under certainty can be potentially misleading.

The contribution of this study provides useful insights into the use of INDEA as a modeling tool to aid managerial decision-making in assessing efficiency of medical diagnostic laboratories based on sustainable development indicators under uncertainty.

The purpose of this paper is to propose a straightforward model for selecting slightly non‐homogeneous vendors.

In this paper the use of the interval data envelopment analysis (DEA) is suggested. The bounds of intervals are constant and can be obtained by various estimation techniques. The interval DEA model provides for the decision making units (DMUs) with missing values a lower and an upper bound of their efficiency score corresponding to their most favorable and unfavorable option.

Employing the proposed method for selecting slightly non‐homogeneous vendors largely reduced practical difficulties for vendor selection. This method does not exclude any vendor from the selection problem. For all the vendors it provides bounds of the efficiency scores depended on the particular data values that the vendors with missing data assign within the intervals so to maximize their efficiency score.

The proposed model considers a slightly non‐homogeneous situation for vendor selection. The proposed approach is driven by multiple criteria. The joint consideration of multiple criteria in a slightly non‐homogeneous environment helps managers select vendors using a comprehensive approach that goes beyond just purchase costs.

This paper is believed to be the first to discuss the problem of slightly non‐homogeneous vendor selection with respect to interval mathematics.

Competition in the banking sector is more complex than in the past, and survival has become more difficult than before. The purpose of this paper is to propose a grey methodology for evaluating, clustering and ranking the performance of bank branches with imprecise and uncertain data in order to determine the relative status of each branch.

In this study, the two-stage data envelopment analysis model with grey data is applied to assess the efficiency of bank branches in terms of operations. The result of grey two-stage data envelopment analysis model is a grey number as efficiency value of each branch. In the following, the branches are classified into three grey categories of performance by grey clustering method, and the complete grey ranking of branches are performed using “minimax regret-based approach” and “whitening value rating”.

The results show that after grey clustering of 22 branches based on grey efficiency value obtained from the grey two-stage DEA model, 6 branches are assigned to “excellent” class, 4 branches to “good” class and 12 branches to “poor” class. Moreover, the results of MRA and whitening value rating models are integrated, and a complete ranking of 22 branches are presented.

Grey clustering of branches based on grey efficiency value can facilitate planning and policy-making for branches so that there is no need to plan separately for each branch. The grey ranking helps the branches find their current position compared to other branches, and the results can be a dashboard to find the best practices for benchmarking.

Compared with traditional DEA methods which use deterministic data and consider decision-making units as black boxes, in this research, a grey two-stage DEA model is proposed to evaluate the efficiency of bank branches. Furthermore, grey clustering and grey ranking of efficiency values are used as a novel solution for improving the accuracy of grey two-stage DEA results.

As supply chain excellence matters, designing an appropriate health-care supply chain is a great consideration to the health-care providers worldwide. Therefore, the purpose of this paper is to benchmark several potential health-care supply chains to design an efficient and effective one in the presence of mixed data.

To achieve this objective, this research illustrates a hybrid algorithm based on data envelopment analysis (DEA) and goal programming (GP) for designing real-world health-care supply chains with mixed data. A DEA model along with a data aggregation is suggested to evaluate the performance of several potential configurations of the health-care supply chains. As part of the proposed approach, a GP model is conducted for dimensioning the supply chains under assessment by finding the level of the original variables (inputs and outputs) that characterize these supply chains.

This paper presents an algorithm for modeling health-care supply chains exclusively designed to handle crisp and interval data simultaneously.

The outcome of this study will assist the health-care decision-makers in comparing their supply chains against peers and dimensioning their resources to achieve a given level of productions.

A real application to design a real-life pharmaceutical supply chain for the public ministry of health in Morocco is given to support the usefulness of the proposed algorithm.

The novelty of this paper comes from the development of a hybrid approach based on DEA and GP to design an appropriate real-life health-care supply chain in the presence of mixed data. This approach definitely contributes to assist health-care decision-makers design an efficient and effective supply chain in today’s competitive word.

Productivity improvement is key to sustainability performance improvements of organizations. In a real-world scenario, the nature of inputs and outputs is likely to be imprecise and vague, leading to complexity in comparing firms' efficiency measurements. Implementation of fuzzy-logic based measurement systems is a method for dealing with such cases. This paper presents a fuzzy weight objective function to solve Data Envelopment Analysis (DEA) CCR model for measuring paper mills' performance in India for 15 years.

An integrated methodology is proposed to solve DEA models having fuzzy weights. The fuzzy DEA methodology is an extended version of the DEA approach that researchers have used for performance measurement purposes in imprecise and vague scenarios. The ecological performance of the paper industry is evaluated, considering some desirable and undesirable outputs. The effect of non-discretionary input on the performance of a paper mill is also analyzed.

Analysis suggests that the productivity of the paper industry is improving consistently throughout the period. The comparative evaluation of methods suggests that a diverse cluster of DMUs and integration of DEA with the fuzzy logic increases the diversity in the efficiency score while DEA-DE imitates the results of CCR DEA.

Proposed a fuzzy DEA-based analytical framework for measuring the paper industry's ecological performance in an imprecise and vague scenario. The model is tested on data from the paper industry in a developing country context and comparative performance analysis using DEA, fuzzy DEA and DE algorithm is done.