Weight Restrictions and Free Production in Data Envelopment Analysis

It is known that the incorporation of weight restrictions in models of data envelopment analysis may result in their infeasibility. In our paper we investigate this effect in detail. We show that the infeasibility is only one of several possible outcomes that point to a particular problem with weight restrictions. For example, the use of weight restrictions may also lead to zero or negative efficiency scores of some units. Removing problematic units from the data set does not necessarily remove the underlying problem caused by the weight restrictions and only makes it undetected. We prove that all such problems arise when weight restrictions induce free or unlimited production of outputs in the underlying technology. This is unacceptable from the production theory point of view and indicates that the weight restrictions need reassessing. We develop analytical criteria and computational methods that allow us to identify the above problematic situations.