Advertising and service investment can enhance brand goodwill to increase the sales of branded goods. However, the impact of advertising and services on brand goodwill is not immediate but delayed. At the same time, due to the different service characteristics provided by various channels, the phenomenon of bidirectional free-riding occurs. Therefore, this paper studies the dynamic cooperation between service and advertising in the O2O (online to offline) supply chain dominated by brand owners and explores the impacts of advertising, service delay and service free-riding among channels on the dynamic cooperation decisions of the O2O supply chain. A differential game model between brands and retailers is constructed by incorporating the delay effect and the bidirectional free-riding phenomenon. The optimal advertising and service strategies and performance problems of O2O supply chain enterprises under a centralized decision, brand cost-sharing decision and bilateral cost-sharing decision are compared and analyzed. The influence of delay time, showrooming and webrooming effects on the profit of each firm is investigated by example. The results show that the service strategy, advertising strategy and brand goodwill of the O2O supply chain members are optimal under a centralized decision. Still, the supply chain profit is not necessarily optimal under the delay time, showrooming and webrooming effect coefficients. Bilateral cost-sharing contracts can achieve Pareto improvement of supply chain performance. Appropriate setting of a bilateral cost-sharing ratio can adjust the adverse effects of delay and bidirectional free-riding. The long-term strategies to deal with the delay and bidirectional free-riding phenomena are as follows: the bilateral cost-sharing contract can improve corporate profits. Setting the wholesale price, online direct-selling price and service-sharing ratio by brand owners can effectively promote retailers’ investment in service, achieving a win-win situation. Retailers maintain high pricing and service levels to enhance the brand premium ability of physical stores and achieve long-term development.
In this article, we construct a three-stage supply chain model using a system of differential equations to reveal the interplay among producers, distributors, and end customers. On the one hand, information about the products and production is exchanged between each stage in the supply chain system. Such information affects the behaviors of each stage. On the other hand, the transport of products between the stages of the supply chain affects the behavior of the system. Our findings are summarized as follows: First, we find that the supply chain model is a system with four chaotic attractors. Second, we explore the synchronization of such a chaotic system. Third, according to the characteristics of the chaotic system, we design a variety of simple control laws to realize the synchronization of two chaotic systems with the same structure. These control laws for the chaotic system are proved to realize local asymptotic synchronization or global exponential synchronization. Numerical simulations are conducted to confirm that the designed controls work well.
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