An enumeration algorithm for integer-valued data envelopment analysis

Abstract

Data envelopment analysis (DEA) models assume real-valued inputs and outputs, but on many occasions, some inputs and/or outputs can only take integer values. In these cases, using DEA models can result in misleading efficiency assessments and inaccurate performance targets. In this paper, we propose an enumeration algorithm for computing efficiency scores and performance targets of decision-making units with integer value inputs/outputs. In the presented algorithm, we do not use any of the mixed integer linear programming (MILP) models that are used in previous studies. We show that the result of our algorithm and that of the MILP model presented in this context is the same. We also generalize our algorithm for different types of returns to scale as well as for the hybrid setting with real-valued data.

Trade‐offs in integer data envelopment analysis

“…Alirezaee and Rafiee Sani () proposed an NA method that computed efficiency scores and performance targets without solving any integer‐programming problems. They proved that the NA method has the same result as the MILP model while requiring less computation.…”

“…Kazemi Matin and Kuosmanen () generalized the IDEA model in different types of return‐to‐scales. On the other hand, Alirezaee and Rafiee Sani () proposed a numeration algorithm (NA) that computed efficiency scores and performance targets for integer‐valued DEA without solving any integer‐programming problems.…”

“…An MILP model can be solved by integer‐programming solvers. In the following, we improve the NA proposed by Alirezaee and Rafiee Sani () and present an improved NA (INA) method for solving IDEA models. Finally, we present a generalized INA method for solving the IDEA‐TO model.…”