Effects of excluding the column being scored from the Data Envelopment Analysis envelopment Linear Programming technology matrix

The reformulation of the envelopment linear programs in DEA to score a decision making unit (DMU) by excluding the corresponding column from the technology matrix raises several theoretical and computational questions. This idea appears natural and has been proposed before, but only recently has it appeared in published form. Several issues associated with this modification to standard DEA analysis remain to be formally and comprehensively explored. One is the feasibility of the resultant LPs which, as it turns out, is not guaranteed under this modification in some of the DEA models. Therefore, the status of the DMU for which the LP is infeasible needs to be resolved. Other issues include the formal equivalence relation between the modified and standard formulations; the impact on the problem of pervasive degeneracy in the LPs and the interpretation of the optimal solutions. This paper investigates these issues and others so as to provide both a firm theoretical basis for the proposed modification in all four convexified free-disposability DEA models and a thorough analysis of the associated effects.