Sensitivity and stability analysis on the k-level of efficiency score relative to interval data

In data envelopment analysis, efficient DMUs are important at first because they define efficient frontier. When the input and output variables of DMUs are interval, the efficiency can be interval that is investigated the lower bound and upper bound from pessimistic and optimistic view respectively. The current paper first represents an algorithm to determine the k-level of decision making units with interval inputs and outputs and then presents a new sensitivity analysis method for a category of DMUs with interval inputs and outputs and finds the stability radius for all efficient DMUs by combining some classic DEA models and with the condition so that the efficiency score of efficient DMU remain unchanged. In the follow, the maximum quantity of data perturbations is obtained so that all first level efficient DMUs remain at the same level. We employed two example for performing algorithm and applied example of twenty branches of Tehran social security insurance organization for obtain maximum alpha and stability radius in our new sensitivity analysis model.