Efficiency evaluation with strong ordinal input and output measures

Data envelopment analysis (DEA) evaluates the relative efficiency of decision making units (DMUs) with multiple inputs and outputs. When inputs and outputs are only known as bounded data or in ordinal relations, the standard DEA model becomes a non-linear and non-convex program. Such a non-linear DEA model can still be solved by standard DEA models via converting bounded and ordinal inputs/outputs into exact data. The current paper shows that caution should be paid when strong ordinal inputs and outputs are present. Models are developed to identify the benchmark in selecting a positive scalar used in converting weak ordinal relations into strong ones. It is shown that extreme-efficient DMUs remain efficient when weak ordinal input/output relations are replaced by strong ones. The paper is illustrated with an application to a Korea telecommunication company.