The paper proposes a knowledge innovation performance model by the dynamic data envelopment analysis with slacks-based measure approach for evaluating the effectiveness of 30 regional knowledge innovation activities in China from 2010 to 2016. In recent years, China has paid more attention to knowledge innovation activities, as central and local governments have pushed on with their innovation projects by lots of investment whatever the difficulties may be. Decision-maker is usually interested in judge its knowledge innovation performance relative to target benchmark by exploring whether one provincial administration region performs better among others and/or if the growth of economy will be benefited greatly by the knowledge innovation activities. To acquire the managerial insight about this issue from a comprehensively designed performance evaluation model, knowledge innovation activity is conceptualized as an intertemporal production process. Invention patent and regional gross product are imposed on desirable outputs, highlighting the need for knowledge economy. The empirical result shows that knowledge innovation has a positive effect on economic development. At the same time, decision-maker should be interest in the economic effect of patents’ type and quality. The government should then encourage new technical applications with greater commercial value from a market-oriented perspective, in order to benefit the most from the innovation process in the short-run.

Centralized safety stock in a periodic replenishment system which consists of one central warehouse and m regional warehouse can reduce backorders allocating the centralized safety stocks to regional warehouse in a certain instant of each replenishment cycle. If the central warehouse can not monitoring inventories in the regional warehouse, then we have to predetermine the instant of allocation according to demand distribution and this instant must be same for all different replenishment cycle. However, transition of inventory level in each cycle need not to be same, and therefore different instant of the allocation may results reduced shortage compare to the predetermined instant of allocation. In this research, we construct a dynamic model based on the assumption of monitoring inventories in the regional warehouse everyday, and develop an algorithm minimize shortage in each replenishment cycle using dynamic programming approach.