Allocation models for DMUs with negative data

The formulas of cost and allocative efficiencies of decision making units (DMUs) with positive data cannot be used data. On the other hand, these formulas are needed to analyze the productivity and performance of DMUs with negative data. To this end, this study introduces the cost and allocative efficiencies of DMUs with negative data and demonstrates that the introduced cost efficiency is equal to the product of allocative and range directional measure efficiencies. The study then intends to extend the definition of the above efficiencies to DMUs with negative data and different unit costs. Finally, two numerical examples are given to illustrate the proposed methods