Efficiency measurement of DMUs with undesirable outputs under uncertainty based on the directional distance function: Application on bank industry

We employ a method that incorporates both direct and indirect approaches based on a directional distance function. In the proposed model, which is based on constant returns to scale, inputs are assumed to be constant. Hence, the presented model is output-oriented. As both desirable and undesirable interval outputs are concerned in this study, we present two evaluation approaches to address the uncertainty problem. First, a lower bound and an upper bound for efficiency are proposed based on the interval approach, and then all units are divided into three categories. It is possible that the model may not remain feasible when data ranges over an interval, and since the data ranges across a bounded, closed, convex set, the robust approach can be adopted for the assessment of decision making units. In this method, unlike the interval approach, the efficiency value calculated for DMUs is certain, and the robust optimal solution is yielded by the proposed level of conservatism for interval parameters. In fact, it calculates the worst optimal solution. In addition, the results of both methods are analyzed and compared in a simple numerical example. Various branches of the National Bank of Iran in Ardabil, Iran, are also evaluated.