A Malmquist productivity index for network production systems in the energy sector

In this paper, a method based on network data envelopment analysis (DEA) is proposed to measure the efficiency and effectiveness of decision making units (DMUs). In this regard, a version of the Malmquist productivity index is designed to accommodate network DEA structures. In this type of environments, sub-DMUs are considered when assessing the efficiency of the main DMU, which helps evaluating the internal structure of the DMUs. The proposed method is applied to measure the productivity of several Iranian oil refineries. After identifying the main factors determining the productivity of these refineries, the operation of nine of them is analyzed using data from the 2015–2016 period. The results show that the management of resource utilization, particularly capital and energy, is inappropriate and investment insufficient. In particular, investment does not aim at upgrading the technology level, despite the fact that the depreciation rate of capital facilities is particularly high in this industry. This particular feature highlights the need to increase the rate of investment in order to replace the depreciated capital