Evaluating the Efficiency of Firms with Negative Data in Multi-Period Systems: An Application to Bank ‎Data

Data Envelopment Analysis (DEA) is a mathematical technique to evaluate the performance of firms with multiple inputs and outputs. In conventional DEA models, the efficiency scores of Decision Making Units (DMUs) with non-negative inputs and outputs are evaluated in a special period of time. However, in the real world there are situations wherein performance of firms must be evaluated in multiple periods of time while negative data are present; for this matter the current paper proposes an approach for assessing the efficiency of multi-period systems in the presence of positive and negative measures. To illustrate, the average efficiency of firms with some negative measures are calculated in multi-period production systems. The suggested approach utilizes the Semi-Oriented Radial Measure (SORM) model (Emrouznejad et al. \cite{4}) for incorporating some negative factors (inputs and outputs) and determining the efficiency of multi-period production systems. A real world data set related to banking sector is used to illustrate and clarify the proposed approach.