Identification of congestion by means of integer-valued data envelopment analysis

• We focus on congestion for integer-valued DEA.
• The associated production possibility set (PPS) is derived.
• Mixed integer programming (MIP) model is used to compute efficiency scores.
• The solutions of the MIP model are used in evaluating the presence of congestion.

In traditional Data Envelopment Analysis (DEA) all inputs and outputs are assumed to take real values. However, this is not realistic in many practical situations and in some applications we may need to work with integer variables and parameters. Once we assume that the variables can take only integer values, we may need to review different concepts of DEA. In this paper we focus on congestion for integer-valued DEA. After introducing the preliminaries and axioms that we need to establish our models, we derive the associated production possibility set (PPS). This step is followed by introduction of a mixed integer programming (MIP) model to compute efficiency scores. More precisely, the solutions of the MIP model is used in evaluating the presence of congestion and in identifying the reasons. Finally, we apply our approach on a couple of empirical examples and report the results.