Assessing environmental and operational efficiencies: a multi-objective optimisation problem in a two-stage network data envelopment analysis

Abstract

Abstract The environmental efficiency of industries plays an important role in economic development of countries. Accordingly, dividing the internal network structure of industries into two sub-processes, including green and operational stages enables decision-makers to assess both of the efficiencies simultaneously. Such assessment can be implemented using a non-parametric methodology termed data envelopment analysis (DEA). Standard DEA models consider the whole system of decision-making units (DMUs) as a single process (i.e., black-box). The black-box approach ignores modelling of the internal network structure of the assessed DMUs. This issue tackled by network DEA models since it considers the internal network structure of DMUs. In the network DEA, the efficiency evaluation of system stages is essential to identify its overall efficiency, resulting to a multi-objective optimisation problem. Therefore, the network DEA is a widely welcomed methodology proposed for solving multi-objective problems. This paper assesses the operational and environmental efficiencies of a network structure system by converting the multi-objective optimisation problem into a linear single objective function. In this investigation, a technique of tri-objective function problem is proposed. The proposed technique transforms into a single objective function by keeping one objective function and shifting the other two objective functions into the model’s constraints. The applicability and usefulness of the proposed technique have been tested using a data set of 20 industries. The developed approach provides valuable evaluations to decision-makers to rank DMUs by considering their green and operational efficiency simultaneously.