Special Types of Data

In the production process physical inputs are consumed to produce physical outputs. All the data are therefore positive real numbers, and the conventional DEA models are based on this requirement. However, in many applications the inputs and outputs may not be physical factors, and thus the data are not necessarily positive real numbers. For example, if profit is used as an output then it can be negative, although the physical quantity of output is always positive. Another situation is that the physical quantities of the inputs consumed by the DMUs are ordered in ranks, or the abilities of different persons (considered as DMUs) can only be ranked, without real term measures. In these cases the data only reflects the relative differences among the DMUs, instead of the absolute differences represented by the conventional measures. A similar case is that the service level provided by a DMU cannot be evaluated by any measures, and is only subjectively expressed by linguistic terms, such as excellent, good, acceptable, and unacceptable. Data of these three types are referred to as negative, ordinal, and qualitative, and Sects. 7.1–7.3 will introduce models for handling these.