A mixed-objective integer DEA model

Traditional efficiency studies using data envelopment analysis (DEA) models considered all input and output variables as continuous, which appears to be unwarranted. Some integer-valued DEA models have been proposed for dealing with the integral constraints in many cases, such as environmental performance measurement, Olympics efficiency assessment, hotel performance evaluation and so on. In existing integer-valued DEA models, the focus is on either input-oriented projection of an inefficient DMU onto the production frontier that aims at reducing input amounts as much as possible while keeping at least the present output levels, or output-oriented projection that maximizes output levels under at most the present input consumption. The present paper develops an integer-valued DEA model that deals with input excesses and output shortfalls simultaneously in a way that maximizes both. An empirical example in the literature is re-examined to compare the DEA model developed here with existing real and integer valued approaches.