Most productive scale size of China's regional R&D value chain: A mixed structure network

This paper offers new mathematical models to measure the most productive scale size (MPSS) of production systems with mixed structure networks (mixed of series and parallel). In the first property, we deal with a general multi-stage network which can be transformed, using dummy processes, into a series of parallel networks. In the second property, we consider a direct network combined with series and parallel structure. In this paper, we propose new models to measure the overall MPSS of the production systems and their internal processes. MPSS decomposition is discussed and examined. As a real-life application, this study measures the efficiency and MPSS of research and development (R&D) activities of Chinese provinces within an R&D value chain network. In the R&D value chain, profitability and marketability stages are connected in series, where the profitability stage is composed of operation and R&D efforts connected in parallel. The MPSS network model provides not only the MPSS measurement but also values that indicate the appropriate degree of intermediate measures for the two stages. Improvement strategy is given for each region based on the gap between the current and the appropriate level of intermediate measures. Our findings show that the marketability efficiency values of Chinese R&D regions were low, and no regions are operated under the MPSS. As a result, most Chinese regions performed inefficiently regarding both profitability and marketability. This finding provides initial evidence that the generally lower profitability and marketability efficiency of Chinese regions is a severe problem that may be due to wasted resources on production and R&D.