Two-stage data envelopment analysis based on interval data

Measuring the performance of a production system has been an important task in management for purposes of control, planning, etc. One technique widely applied to measure the relative efficiency of a set of production systems, or decision making units (DMUs), which utilize the same inputs to produce the same outputs, is data envelopment analysis (DEA). Conventionally, the system is treated as a black box, in which only inputs and outputs of the black box are considered in measuring the efficiency. The performance of the component processes interacting with each other in the system are not considered. In some situations (in real applications) of DEA applications, there are Decision Making Units (DMUs) which have two-stage structure. In the previous two-stage models have been assumed that all inputs and outputs of DMUs are exactly known and this assumption may not be true (i.e. some or all of inputs and outputs may be imprecise). This paper proposes a method to determine efficiency of two-stage DMUs with interval inputs and outputs. Then illustrates the proposed method using an example.