One of the major concerns of managers in the field of health is the optimal allocation of manpower and resources; So in this study, to the quality of provided services in this area not to be damaged, we have used the data envelopment analysis (DEA) model to determine the efficiency of hospital emergency departments and possible improvements. Traditional DEA models do not seek to reduce undesirable outputs and increase undesirable inputs, so in this study, decision-making units (DMUs) effect on efficiency has also been investigated in addition to determining the efficiency of decision-making units (DMUs) with the presence of some undesirable output components. To do this, first, the set of proper production possibilities has been defined according to the problem assumptions and while examining the performance and ranking with Andersen-Petersen and Super-SBM models, a new method has been provided to determine the unfavorable performance of some output components in decision-making units. We have specified the effect of undesirable output on determining efficiency. We have also provided a real example of 30 hospital emergencies for 5 desirable inputs and 4 desirable outputs and one undesirable output, solved that example, and determined the efficiency score. Manuscript profile

One of the major concerns in healthcare management is the optimal allocation of staffing and resources. The global crisis created by the COVID-19 Pandemic has created extreme strains both on the staffing and the resources available to the healthcare systems. It has geometrically added to the number of patients seeking health services. In addition, the Pandemic has dramatically increased the rate of mortality in the hospitals in an unprecedented way. Therefore, in this research, in order not to sacrifice the quality of the services provided, we have used Data Envelopment Analysis (DEA) model to determine the efficiency of the emergency departments in the hospitals and the possible improvements that could be made to them. As traditional DEA models do not seek to reduce the undesirable outputs and increase the undesirable inputs, in addition to determining the efficiency of decision making units (DMU) despite some undesirable input components, the effect of these units on performance is investigated. To this end, considering the problem assumptions, first, a set of proper production possibilities is defined. Finally, a new method is introduced to determine the system’s performance in the presence of some undesirable input components. The impact of undesirable components on determining efficiency is specified, and a real example is provided consisting of emergency rooms in 30 hospitals, in which five desirable inputs and four desirable outputs along with one undesirable input are considered. The example is solved using the presented model, and the efficiency scores are determined. Manuscript profile

Data envelopment analysis is always considered as a non-parametric method for measuring the efficiency of a set of decision units. The efficiency number obtained from standard models is a criterion for comparing the performance of each decision unit with other units. Despite the many strengths of these models, one of their weaknesses is the lack of distinction between efficient units. Also, these models do not pay attention to the internal structure of the units and have a black box view. To solve these problems, relational data envelopment analysis models are used, which are much more cost-effective in terms of time and cost; But these models are static and do not take time into evaluation. In this paper, a method has been proposed for grading of the decision making units with multi- period two stages network structure using relative data envelopment analysis. Three different perspective are introduced for assessment of efficiency in time periods via relative data envelopment analysis. Proportionate with each perspective, an efficiency number is obtained for any decision making unit. Then three efficiency numbers obtained in the mentioned method is combined with Shannon entropy method and a total efficiency criterion is defined for each unit. Finally, this measure is considered as the main indicator for the units grading. The results of implementation of the mentioned algorithm on the real example and comparison with the similar methods clarify the strength of this algorithm. Manuscript profile