OICC Press International Journal of Mathematical Modelling & Computations 2228-6233 14 1 2024 03 31 Nonhomogeneous DMUs in DEA: A Directional Distance Function Approach 1 13 10.71932/ijm.2024.1118735 EN Mona Barat Department of Mathematics,Mahshahr Branch, Islamic Azad University, Mahshahr, Iran Ghasem Tohidi Department of Mathematics,Central Tehran Branch, Islamic Azad University, Tehran, Iran Journal Article 2024 03 31 Data envelopment analysis (DEA) provides performance evaluation for a set of homogeneous decision making units (DMUs) in the sense that all DMUs evaluated with the same criteria setting. In some settings, however, the assumption of having a common input and output bundle may not hold. Such can occur in universities, for example, since they may have different departments, or in hospitals where have different wards. This motivates to the issue of how to fairly evaluate efficiency when inputs and outputs configurations are different. This paper proposes a three-process methodology that aims at evaluating of a set of DMUs when the requirement of homogeneity among inputs and outputs is relaxed. In the first step, based on the duality theory a multiplier directional distance function (DDF) model is developed to determine an appropriate split of inputs and output. In step 2, the efficiency of a DMU is evaluated in terms of each scaled down inputs and outputs. Finally, the overall efficiency score of a DMU is viewed as a weighted combination of a set of product lines efficiencies. To demonstrate the validity and practicability of the proposed method, we apply it to evaluate the performance of a hypothetical data set. The results show that the methodology has the ability to discriminate performance for data with nonhomogeneous inputs and outputs.