Suitability and redundancy of non-homogeneous weight restrictions for measuring the relative efficiency in data envelopment analysis

Weight restrictions are non-homogeneous if they are formulated as linear ‘less than or equal to’ inequalities with a non-zero constant on the right-hand side. Absolute weight bounds are typical examples. It has recently been shown that, in the presence of such restrictions, the fractional linear data envelopment analysis (DEA) model and its linear forms may incorrectly evaluate the maximum relative efficiency of the assessed unit. This paper investigates the problem further, and identifies certain types of non-homogeneous restrictions that do not cause the observed error. Thus the relative efficiency is always assessed correctly if, in the same CCR model, no positive lower bounds are imposed on any of the input weights and no upper bounds are imposed on any of the output weights. The redundancy of certain types of weight restrictions in DEA models is also considered. Based on this, the traditional use of small positive constants to separate weights from zero in DEA models is questioned.