This paper is concerned with application problem of optimal control to a class of dynamic advertising models with multiple delays. Here, a dynamic model with state and control delays is introduced to describe the impacts of advertising delayed and memory effects on the evolution of brand goodwill. In the decentralized and centralized systems, the optimal advertising strategies of supply chain members are presented by utilizing the nonzero-sum differential game governed by differential equation with multiple delays in state and control variables. Special effort is made to analyse the geometrical shapes of advertising strategy and provide the optimal decision structure of supply chain system. Furthermore, nonzero-sum stochastic differential game is applied to explore the dynamic advertising decision problems of supply chain system with the multiple delays and stochastic cases. Finally, numerical examples are exploited to illustrate the effectiveness of the proposed results.

The strengthening scientific and reasonable quantitative evaluation of innovation performance of low-carbon technology breakthrough innovation network in manufacturing industry under the background of economic globalization is of important significance, which can enrich relevant theoretical system of low-carbon technology breakthrough and improve the core competitiveness of Chinese manufacturing industries. In this paper, the scientific and reasonable quantitative evaluation of the innovation performance of low-carbon technology breakthrough innovation network is firstly determined as a dynamic (timevarying) evaluation problem, which involves multi-source influencing factors. Note that many evaluation objects in the innovation performance of an innovation network are gray, ambiguous and dynamic variables, which are difficult to be quantified and the collected industrial data has certain discreteness and fluctuation. Hence, a fuzzy clustering analysis on influencing variables of innovation performance of low-carbon technology innovation network is carried out via the sampling data from 28 manufacturing industries during 2011-2016. Moreover, an innovation performance evaluation model for low-carbon technology innovation network is constructed through analytic hierarchy process (AHP), grey theory and fuzzy clustering analysis. Based on this model, the qualitative and quantitative evaluations of innovation performances of the innovation network before and after low-carbon technology breakthrough are realized. The results show that the low-carbon technology breakthrough innovation has a positive effect on improving the development level of manufacturing industry. In addition, the construction performance evaluation model not only decreases the influences of subjective factors by combining qualitative analysis with quantitative analysis, but also applies the grey theory innovatively to determine the membership matrix. It realizes accurate, systematic and scientific evaluation of the innovation performance of the low-carbon technology breakthrough innovation network in the manufacturing industries. Finally, the research conclusions provide the theoretical and practical references to the strategic arrangement of the low-carbon technology breakthrough innovation in Chinese manufacturing industries. INDEX TERMS Low-carbon technology breakthrough innovation; Innovation network; Innovation performance; Chinese manufacturing industries; AHP I. INTRODUCTION With the continuous transition of global technological innovative ability, the innovation-driven development has be

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According to the functional structure and design structure of the manufacturing products, a lowcarbon evaluation index system is established for product maintenance and support system, where the particularity of the working environment of manufacturing products, the maintenance ability and the support tasks of equipment manufacturing products are all considered. In particular, the expert evaluation method and the empirical analysis of factory technologists are used for a single index, and a recursive algorithm is given. According to the principle of the maximum membership degree, the merits and demerits based on the membership degree of the comments are evaluated, and both the multi-level index system and the fuzzy comprehensive evaluation method are combined. In addition, a comprehensive evaluation method, i.e. Multi-level Fuzzy Correlation Clustering Analysis (MFCCA) with a clear idea, is given for the low-carbon evaluation of the manufacturing products. Finally, the correctness, effectiveness and superiority of the proposed method are verified via the test experiments of an electric machine factory in the manufacturing industry. ARTICLE HISTORY