Abstract
AbstractIf production trade‐offs—which represent simultaneously feasible exchanges in the inputs and outputs of decision‐making units (DMUs)—are added to an integer production possibility set (IPPS), a new IPPS is produced; conventional axioms of production do not generate a new IPPS, however. This paper develops the axiomatic foundation for data envelopment analysis (DEA) for integer‐value inputs and outputs in the presence of production trade‐offs by introducing a new axiom of “natural trade‐offs.” First, a mixed‐integer linear programming formula called an integer DEA trade‐off (IDEA‐TO) is presented for computing efficiency scores and reference points. The numeration algorithm (NA) method presented in this concept is improved, and an improved numeration algorithm (INA) method for solving integer DEA (IDEA) models is developed. Finally, comparison between the two methods and a generalized INA method for solving the IDEA‐TO model are presented.
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