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The purpose of this paper is to introduce an innovative data envelopment analysis (DEA) model entitled “Non‐binary Arithmetic Operator Dual‐role” (NAOD) under free disposability assumption for selecting the refrigerated containers in cold chain management (CCM).

In classical DEA models, it is assumed that all of input and output variables play a certain role. However, in some cases, some variables play both input and output roles, simultaneously. These variables in DEA are called “dual‐role” factors. This study introduces a new approach to deal with these factors in the process of evaluating a set of homogeneous refrigerated containers, which is based on Free Disposal Hull (FDH) (one of the DEA models). However, in previous dual‐role models, this variable is considered as a binary variable. In this paper, a partial role for dual‐role factors is considered.

The main findings of this paper are: for the first time, the NAOD model is developed for the container selection problem in the context of CCM and the dual‐role factors are considered for the container selection problem. The NAOD model determines partial role of dual‐role factors and can consider multiple dual‐role factors. For the first time, the container selection problem is solved by an FDH model. The result of NAOD model is validated by genetic algorithm.

The paper makes a sufficient contribution to the practice of operations research. It is the first study which applies advanced DEA models for selecting the containers in the context of the CCM. To the best of the authors' knowledge, there is no other reference that deals with container selection in the context of CCM in the presence of dual‐role factors.