Measuring efficiency in a general production possibility set allowing for negative data

Conventional data envelopment analysis (DEA) models for measuring efficiency are developed for positive data. However, difficulties are encountered when data has negative values. Several models have been proposed to calculate efficiency in the presence of negative data. While efficiencies can be calculated from these models, most of them are biased and lack underlying supporting theories. This paper proposes a generalized radial model defined on a more general production possibility set that only requires the aggregate input and aggregate output to be positive. The model can be used to identify unrealistic production processes. It works under the assumptions of both constant and variable returns to scale. It can thus be used to measure scale efficiency in addition to the conventional productive efficiency. This model can also be extended to network systems, and the simplest extension of the two-stage system is discussed. The property of the conventional two-stage DEA model in which the system efficiency is the product of the two stage efficiencies is also satisfied by the generalized radial model. A case of twenty-nine supply chains is used to demonstrate how the proposed model can be applied to calculating efficiency for a conventional whole-unit (black-box) system and a two-stage system.