考虑服务流的产品服务供应链网络均衡模型

产品服务供应链在向客户制造高质量产品的同时，也提供了产品全生命周期的专业服务，服务的嵌入增加了供应链协调的复杂性。考虑产品服务的双重需求，在分析各主体的运作行为的基础上，构建了包括多个制造商和多个销售商的多主体供应链网络；运用变分不等式刻画了制造商层、销售服务集成商层和需求市场的最优运作行为及其达成均衡的条件；最后，通过修正投影算法对数值算例进行了仿真。研究结果表明：产品服务供应链网络中的产品与服务均衡流相互影响，其中，服务水平直接影响到了产品需求；降低产品的售价将有利于服务价格和效益的提升。研究结论进一步印证了在产品服务供应链网络中承载于产品的服务将逐渐成为价值创造的主体。

A Product Service Supply Chain Network Equilibrium Model with Service Flow

Service-oriented manufacturing, as a new advanced manufacturing model formed by the integration of manufacturing activities and service activities, is the mainstream direction of manufacturing transformation and upgrading. On account of service embedding and multi-agent participation, traditional supply chain operation mode is difficult to adapt to the requirements of service-oriented manufacturing, and it is urgent to reconstruct the supply chain network for service-oriented manufacturing. For the service-oriented manufacturing model of product and after-sales service integration, a product service supply chain network including manufacturers, sales service integrators and customers is constructed, and the logistics, service flow and information flow in the network are fully analyzed. There is a problem of equilibrium of interests among the various entities in the new product service supply chain network. Therefore, variation inequalities are used to describe the optimal operation behavior of manufacturers, sales service integrators and demand market and the conditions for achieving equilibrium. Finally, the numerical examples are simulated by the modified projection algorithm, and the equilibrium product flow and value flow in the product service supply chain network are obtained, as well as the equilibrium product price and service price. The results show that product service supply chain network is more complex and diversified than the traditional supply chain operation, which is manifested in the intimate combination of service and logistics, network node interaction and cross-level communication; the level of after-sales service provided by the after-sales service system directly affects the demand for products in the supply chain, while the sales volume of the products provided by the former market constitutes the potential demand for after-sales service in the aftermarket; customers' demand for services mainly comes from sales service integrators, some of which are provided by manufacturers. However, most of the services provided by manufacturers are core and professional services, and the service level is high, which is irreplaceable by sales service integrators.