Two-stage network processes with shared resources and resources recovered from undesirable outputs

Data envelopment analysis (DEA) is an approach for measuring the performance of a set of homogeneous decision making units (DMUs). Recently, DEA has been extended to processes with two stages. Two-stage processes usually have undesirable intermediate outputs, which are normally considered be unrecoverable final outputs. In many real situations like industrial production however, many first-stage waste products can be immediately used or processed in the second stage to produce new resources which can be fed back immediately to the first stage. The objective of this paper is to provide an approach for analyzing the reuse of undesirable intermediate outputs in a two-stage production process with a shared resource. Shared resources are input resources that not only are used by both the first and second stages but also have the property that the proportion used by each stage cannot be conveniently split up and allocated to the operations of the two stages. Additive efficiency measures and non-cooperative efficiency measures are proposed to illustrate the overall efficiency of each DMU and respective efficiency of each sub-DMU. In the non-cooperative framework, a heuristic algorithm is suggested to transform the nonlinear model into a parametric linear one. A real case of industrial production processes of 30 provincial level regions in mainland China in 2010 was analyzed to verify the applicability of the proposed approaches.