Simultaneous estimation of input–output levels under improving efficiency level in an assessment window

Inverse data envelopment analysis technique is a useful tool in planning and management control to estimate the level of input/output of decision-making units to achieve the predetermined efficiency targets. In the real problems, data are time-dependent that also this technique is influenced by this parameter. The current paper studies this technique in a dynamic framework. In fact, the problem of estimating the input and output levels simultaneously is studied when data are time-dependent. This problem is solved using multiple-objective programming tools in the framework of dynamic inverse data envelopment analysis. The proposed models in the current study, unlike other existing models in the literature of inverse data envelopment analysis, can solve the problem of estimating the input and output levels such that the unit maintains or improves its current efficiency level to a pre-defined amount in the assessment window. Necessary and sufficient conditions are derived for the estimation of input and output levels through the linear multiple-objective programming problems. Also, the applicability and limitations of the provided method are explained via a real example of the banking sector on a period of six months. The proposed approach is confirmed according to the obtained numerical results as well.