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In conventional DEA models it has been assumed that each measure status is considered input or output. However, a performance measure in some cases can have input role for some DMUs and output role for others and is known as flexible measure. In this paper new slacks-based FNSBM models are proposed in general two-stage network DEA to determine the relative efficiency of units and the role of flexible measures. Then new radial FNDEA-R models and new slacks-based FNSBM-DEA-R models are developed in the presence of flexible measures based on the ratio of input components to output components or vice versa in the input and output orientation under constant returns to scale in general two-stage network. In our proposed models, flexible measures are determined as input or output to improve performance to maximize the relative efficiency of the DMU under evaluation. The FNDEA-R and FNSBM-DEA-R models versus FNSBM models prevent efficiency underestimation and pseudo inefficiency issues. The status of one flexible measure in the input-oriented and output-oriented FNDEA-R and FNSBM-DEA-R models may have different conclusions. The radial FNDEA and FNDEA-R models have unitsinvariant and the objective function of the FNSBM and FNSBM-DEA-R models are invariant with respect to the units of data. A numerical example is used to illustrate the procedures. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to present a new approach for measuring the performance of n-stage series systems in the presence of uncertain data, which are two challenging issues in evaluating the efficiency of Decision-Making Units (DMUs) using traditional Data Envelopment Analysis (DEA) models. By using a Network DEA model and its dual, as well as using Bertsimas et al.'s robustness technique, two Robust Network DEA have been presented. These models can display a range of DMUs performance with appropriate accuracy. Proposed models were used to determine the efficiency range of Iranian dairy companies' supply chain with three stages. The results show that the proposed models are applicable and effective. Total efficiency bounds are obtained with percentage deviations of 20%, 10% and 5%. The lower bounds have relative errors of 0.39, 0.23 and 0.12 and a correlation coefficient of more than 97%, and the upper bounds have relative error of 1.1, 0.84 and 0.62 and a correlation coefficient of about 90%. Therefore, the proposed model for calculating the lower bound is more accurate. The calculation of the efficiency bounds of the sub-stages also confirms this issue. Finally, the obtained results have been compared with the values obtained through a fuzzy three-stage DEA model, our results have a higher correlation coefficient and more accurate upper bounds. [ABSTRACT FROM AUTHOR]

The distribution of hospital beds can be used as an indicator to assess the distribution of health services. This study aimed to determine and prioritize indicators of hospital bed allocation in Iran. In the first phase of the study, we used a scoping review to identify criteria affecting hospital bed allocation. Then, we applied an expert panel and the Delphi method to localize the criteria. Finally, we carried out Analytic Network Process method based on Decision Making Trial and Evaluation Laboratory technique (DANP), to determine the weight and importance of indicators and to evaluate the causal relationship between them. Based on the scoping review, we identified 75 criteria that influence bed allocation. In 2 Delphi cycles, 28 criteria were selected and included in the DANP phase. The population, the presence of a reference hospital in the region, the type of hospital, the common diseases in the region, and the presence of home care services were the variables that had the most interaction with other variables. The variable of home care services was at the highest level of the causal chain. Bed occupancy rate, average length of stay, waiting list, as well as type and level of the hospital had the highest priority in the allocation of hospital beds. Furthermore, given the importance of home care services, policies should be adopted to expand these services nationwide. The indicators identified in this study will be useful for the development of policies aimed at an equitable allocation of hospital beds. Key Points: The authors identified 75 criteria affecting the distribution of beds through scoping review.The criteria with the highest level of interaction were population, existence of a reference hospital in the area, the type of hospital, common diseases in the area, and existence of home care services.The variable of home care services was at the highest level of the causal chain. [ABSTRACT FROM AUTHOR]

The data envelopment analysis method is commonly used to measure efficiency. An estimate of the relative efficiency of this model is derived by calculating the ratio between inputs and outputs. Data envelopment analysis models can also be applied to network structures due to the extension of these models. Supply Chain Management (SCM) is a novel approach that governed production management in recent years. In complex and dynamic environments, the petrochemical industry requires an investigation system similar to those used by other organizations to inform about its activity's desirability, especially in complex and dynamic environments. This research focused on the petrochemical company supply chain. Laboratory studies, experts, and visits to petrochemical sites were used to identify production processes and determine indicators. After that, they were evaluated with an envelopment model and a coefficient corresponding to the identified petrochemical supply chain structure. The aggregate and componentwise efficiency of the studied units in petrochemical were also examined from 2016 to 2019. [ABSTRACT FROM AUTHOR]

In this paper, while taking into account the cooperative relationships between units, the problem of revenue allocation is considered as a coalitional game. In order for the allocation to be equitable, by relying on the concept of DEA efficiency, a new characteristic function is presented, and then using the concept of the Shapley value, which is a wellrecognized concept in coalitional game theory, a unique solution is obtained for the revenue allocation problem. And finally, to evaluate the equitability of the performed revenue allocation, the Gini coefficient is utilized. A comparison of the Gini coefficient obtained for our method with those of some existing methods showed that our method is more equitable than the previous ones. This demonstrates how impactful the wise and accurate selection of the characteristic function is in the equitability of the results. [ABSTRACT FROM AUTHOR]

As an important concept in data envelopment analysis (DEA), elasticity measure has wide theoretical and practical applications in formulating various economic concepts. Anchor points also appear to be particularly interesting and highly useful in DEA, especially for recognizing a decision making unit (DMU) as a benchmark. This paper is an attempt to use left-and right-hand elasticity measures to present a novel definition (characterization) for anchor points. The study results reveal that if there exists an increase in a bundle of input with no rate of change in a bundle of output or if there is a decrease in a bundle of output, but a bundle of input has no rate of change, then such an extreme point is the anchor point. [ABSTRACT FROM AUTHOR]

Purpose: The current paper tries to determine the type of returns to scale in a decision-making unit under the condition that integer-valued inputs or outputs are present. Methodology: This paper introduces radial models for determining the value and type of Returns to Scale (RTS) in 4 scenarios, including single integer-valued input -- single real output (scenario one), mixed inputs -- exclusively real outputs (scenario two), exclusively integer-valued inputs -- exclusively real outputs (scenario three), and exclusively integer-valued inputs -- exclusively integer-valued outputs (scenario four); in each scenario, the values of the left RTS and right RTS are determined, and the RTS type is then determined on that basis. Finally, by presenting three examples based on two scenarios, namely single integervalued input -- single real output and single integer-valued input -- single integer-valued output, the new method is compared with previous methods using GAMS software, and the conclusions are provided. Findings: The type of returns to scale differs when integer-valued inputs or outputs are present as compared with the case where the inputs and outputs are assumed to have real values. Originality/Value: This study focuses on the value and type of returns to scale for integer-valued data. For this purpose, returns to scale was modeled in 4 scenarios using input-oriented radial models, and in the fourth scenario (exclusively integervalued inputs -- exclusively integer-valued outputs), the modeling was carried out for output orientation as well. The existence of a difference between the results produced by our proposed model and those of the classical model was demonstrated through two examples, one using hypothetical data and the other real-world data. [ABSTRACT FROM AUTHOR]