Relative efficiency measurement: The problem of a missing output in a subset of decision making units

Data envelopment analysis (DEA), as originally proposed by Charnes et al. (1978) viewed the efficiency measurement problem as one wherein each of a set of DMUs uses the same input and output measures, albeit in amounts that vary from one DMU to another. In some situations, however, the assumption that all DMUs use the same measures may fail. While there is a well known literature related to the problems of missing data and ‘zeros’ in the data, we argue that there is a difference between the situation where a DMU commits the resources to produce an output (but fails to do so, or else a non-zero amount exists but is unknown), and the situation where the DMU intentionally does not produce that output. In the current paper we examine the problem of measuring the efficiency of a set of steel fabrication plants wherein a subset of those plants produce one less than the full set of outputs produced by the others. We develop a DEA-type model for handling this missing output problem.