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The purpose of this paper is to present a stochastic p-robust data envelopment analysis (DEA) model for decision-making units (DMUs) efficiency estimation under uncertainty. The main contribution of this paper consists of the development of a more robust system for the estimation of efficiency in situations of inputs uncertainty. The proposed model is used for the efficiency measurement of a commercial Iranian bank.

This paper has been arranged to launch along the following steps: the classical Charnes, Cooper, and Rhodes (CCR) DEA model was briefly reviewed. After that, the p-robust DEA model is introduced and then calculated the priority weights of each scenario for CCR DEA output oriented method. To compute the priority weights of criteria in discrete scenarios, the analytical hierarchy analysis process (AHP) is used. To tackle the uncertainty of experts’ opinion, a synthetic technique is applied based on both robust and stochastic optimizations. In the sequel, stochastic p-robust models are proposed for the estimation of efficiency, with particular attention being paid to DEA models.

The proposed method provides a more encompassing measure of efficiency in the presence of synthetic uncertainty approach. According to the results, the expected score, relative regret score and stochastic P-robust score for DMUs are obtained. The applicability of the extended model is illustrated in the context of the analysis of an Iranian commercial bank performance. Also, it is shown that the stochastic p-robust DEA model is a proper generalization of traditional DEA and gained a desired robustness level. In fact, the maximum possible efficiency score of a DMU with overall permissible uncertainties is obtained, and the minimal amount of uncertainty level under the stochastic p-robustness measure that is required to achieve this efficiency score. Finally, by an example, it is shown that the objective values of the input and output models are not inverse of each other as in classical DEA models.

This research showed that the enormous decrease in maximum possible regret makes only a small addition in the expected efficiency. In other words, improvements in regret can somewhat affect the expected efficiency. The superior issue this kind of modeling is to permit a harmful effect to the objective to better hedge against the uncertain cases that are commonly ignored.

This paper aims to apply a new approach for resource sharing and efficiency estimation of subunits in the presence of non-discretionary factors and partial impacts among inputs and outputs in the data envelopment analysis (DEA) framework.

First, inspired by the Imanirad et al.’s model (2013), the authors consider that each decision-making unit (DMU) may consist of several subunits, that each of which can be affected by non-discretionary inputs. After that, the Banker and Morey’s model (1996) is used for modeling non-discretionary factors. For measuring performance of several subunits, which can be considered as DMUs, the aggregate efficiency is suggested. At last, the overall efficiency is computed and compared with each other.

One of the important features of proposed model is that each output in this model applies discretionary input according to its need; therefore, the result of this study will make it easier for the managers to make better decisions. Also, it indicates that significant predictions of the development of the overall efficiency of DMUs can be based on observing the development level of subunits because of the influence of non-discretionary input. Therefore, the proposed model provides a more reasonable and encompassing measure of performance in participating non-discretionary and discretionary inputs to better efficiency. An application of the proposed model for gaining efficiency of 17 road patrols is provided.

More non-discretionary and discretionary inputs can be taken into consideration for a better analysis. This study provides us with a framework for performance measures along with useful managerial insights. Focusing upon the right scope of operations may help out the management in improving their overall efficiency and performance. In the recent highway maintenance management systems, the environmental differences exist among patrols and other geotechnical services under the climate diverse. Further, in some cases, there might exist more than one non-discretionary factor that can have different effects on the subunits’ performance.

The purpose of this paper was to measure the performance of a set of the roadway maintenance crews and to analyze the impact of non-discretionary inputs on the efficiency of the roadway maintenance. The application of the proposed model, on the one hand, showed that each output in this model uses discretionary input according to its requirement, and on the other hand, the result showed that meaningful predictions of the development of the overall efficiency of DMUs can be based on observing the development level of subunits because of the impact of non-discretionary input.

Providing information on resource sharing by taking into account non-discretionary factors for each subunit can help managers to make better decisions to increase the efficiency.