Rang-adjusted measure: modelling and computational aspects from internal and external perspectives for network DEA

The range-adjusted measure (RAM) as one of the non-radial data envelopment analysis (DEA) models has been broadly used in the assessment of decision-making units (DMUs). In many situations, the DMUs have a multi-component (network) structure, where the output of each component can be used as the input of another component, which is referred to as intermediate output. Various methods with different forms of production possibility sets (PPSs) have been suggested to formulate the intermediate output in efficiency calculations that link network components and each of these methods leads to different efficiency scores. These different forms of PPSs include independent, relational, and cooperative, which can appraise the efficiency of a DMU from internal and external perspectives. This paper aims to clarify the relationship among different forms of PPSs for the network RAM-DEA model from internal and external perspectives by emphasizing the development of a network RAM-DEA model. This study shows that from internal evaluation, a DMU with a network structure may operate efficiently while it is inefficient from external evaluation. This study proves that to evaluate a DMU with a network structure, the cooperative form of PPS is more suitable from both internal and external perspectives. The independent form of PPS does not exactly define the relationships among the components, so it is not recommended for computing the efficiency of a network. Models associated with the relational form of PPS may cause excess supply (waste) in the network, which is not appropriate for internal evaluation. Finally, a real example illustrates the applicability of the presented model.