A new non oriented models for calculating the efficiency of decision-making units in the presence of flexible variables

In assessing the relative efficiency of decision-maker units by classical Data Envelopment Analysis (DEA) models, the status of the data is determined from the input or output points of views. In real issues, there are some data whose statuses are debatable. Some decision making units consider them as input to achieve higher efficiency while some other decision making units consider them as output, but these data are known as flexible variables. Thus, these data are known as flexible variables. Several parametric and non-parametric models have been introduced for categorizing such data. In most of the status-oriented models (input or output based) introduced to determine the status of flexible data, different statuses of a model can produce different results in determining the statuses of the flexible variable. In non-status models, the value of M is also used to select the main constraint and to remove the waste constraints. In these models, by choosing different values for M, different results are achieved in determining the status of the flexible variable, the efficiency and return to scale of decision-making units. To solve these problems in DEA, a non-status model is proposed which, in addition to determining the status of the flexible variable, can obviate the computational error, and the problems caused by the presence of M in the model. The advantages of the proposed model are compared with other models with an empirical example.