Data envelopment analysis of integer-valued inputs and outputs

This paper addresses DEA scenarios whose inputs and outputs are naturally restricted to take integer values. Conventional DEA models would project the DMU onto targets that generally do not respect such type of integrality constraints. Although integer-valued inputs and outputs can be considered as a special case of ordinal inputs and outputs, the use of that type of models has many drawbacks. In this paper a MILP DEA model that guarantees the required integrality of the computed targets is proposed. Scope and purpose Data envelopment analysis (DEA) is a well-known OR technique for evaluating the relative efficiency of a set of similar decision making units (DMU). The number of applications of DEA is large, covering fields as diverse as finance, health, education, manufacturing, transportation, etc. Conventional DEA models are based on Linear Programming and consider continuous inputs and outputs. However, there are many occasions in which some inputs and/or outputs can only take integer values. Normally, it is assumed that the real-valued results of DEA would be rounded somehow ex post. In this paper, a different approach is proposed, consisting in introducing new DEA concepts and models that explicitly take into account integer inputs and outputs, thus guaranteeing ex ante the feasibility of the results.