Profit inefficiency decomposition in a serial-structure system with resource sharing

Previous studies have used overall profit inefficiency (OPI) to assess the overall profit improvement of firms and decomposed OPI into technical and allocative components to identify the specific sources of overall potential gains. Resource sharing among the stages of the network structure system as a type of resource allocation is also a source of increasing system profit; however, this kind of source has not been identified and specified in previous works. Based on network data envelopment analysis (DEA), this study explores the OPI decomposition issue in a three-stage serial-structure system with resource sharing existing among stages. We prove that resource sharing among stages can bring potential gains. Using a multiplicative decomposition method based on the measure of profit ratios, we decompose the OPI into product of technical profit inefficiency (TPI), resource sharing profit inefficiency (RSPI), and free allocation profit inefficiency (FAPI), where the RSPI multiplies by FAPI is consistent with the allocative component in previous studies. A numerical example is used to illustrate our approach, and the results show that the overall potential gains can be decomposed into gains derived from removing technical inefficiency, resource sharing, and free allocation within the whole production possibility set.