Management Research in Iran

Abstract Data Envelopment Analysis (DEA), as a non-parametric and data-driven methodology, is an effective tool for assessing the relative efficiency of a set of decision-making units (DMUs) with multiple inputs and outputs. However, classical DEA models disregard the internal structure of DMUs and treat them as “black boxes.” To overcome this limitation, network DEA has been developed to explicitly model the internal interactions among the components of each DMU. Moreover, in many real-world applications, certain input, output, or intermediate variables are inherently discrete and take integer values, and negative data may also be present. Such characteristics are typically ignored in conventional DEA models and can lead to inaccurate or impractical efficiency estimates. This paper proposes a novel network DEA model based on the directional distance function for two-division series systems, capable of simultaneously handling negative data and integer-valued variables. By defining an appropriate direction vector, the proposed model enables the measurement of system efficiency under both constant returns to scale and variable returns to scale. To demonstrate the capabilities of the proposed model, a real case study involving 29 Iranian supply chains in the medical consumables industry is conducted. The results show that the proposed model not only accurately distinguishes between efficient and inefficient DMUs but also provides projection points that specify the exact pathway for performance improvement in each division. The findings indicate that the proposed approach can serve as a robust and reliable tool for evaluating and enhancing supply chain efficiency, particularly in sensitive industries such as medical consumables.

Abstract Data envelopment analysis (DEA) is an approach to measuring the relative efficiency of a set of decision making units (DMUs) with multiple inputs and multiple outputs using mathematical programming. The traditional DEA, which is based on the concept of efficiency frontier (output frontier), determines the best efficiency score that can be assigned to each DMU. Based on these scores, DMUs are classified into DEA-efficient (optimistic efficient) or DEA-non-efficient (optimistic non-efficient) units, and the DEA-efficient DMUs determine the efficiency frontier. There is a comparable approach which uses the concept of inefficiency frontier (input frontier) for determining the worst relative efficiency score that can be assigned to each DMU. DMUs on the inefficiency frontier are specified as DEA-inefficient or pessimistic inefficient, and those that do not lie on the inefficient frontier, are declared to be DEA-non-inefficient or pessimistic non-inefficient. In this paper, we argue that both relative efficiencies should be considered simultaneously, and any approach that considers only one of them will be biased. For measuring the overall performance of the DMUs, we propose to integrate both efficiencies in the form of an interval, and we call the proposed DEA models for efficiency measurement the bounded DEA models. In this way, the efficiency interval provides the decision maker with all the possible values of efficiency, which reflect various perspectives. A numeric example about Iranian gas companies will be evaluated using the DEA approach with efficient and inefficient frontiers to show its convenience and usefulness.