Abstract:

Terminal logistics delivery efficiency and order response speed are core objectives for logistics companies to maintain market competitiveness and customer loyalty. Faced with differentiated and dynamically emerging category demands， traditional centralized warehousing models exhibit shortcomings such as delayed customer responses and low delivery efficiency. The proactive warehouses are utilized as connection points in a two-level logistics network and a two-stage dynamic vehicle scheduling problem is investigated based on proactive category （TSDVSP-PC）. The problem is described using an undirected graph， where the node set consists of depots， proactive warehouses， and customers. The arc set includes arcs between depots and static customer locations， arcs between depots and dynamic nodes without proactive categories， and arcs between proactive warehouses and dynamic customer nodes with proactive categories. During the distribution process， customers with regular demands are served directly by the depots， while customers with proactive demands are served by nearby proactive warehouses. The problem is modeled as a multi-category vehicle scheduling problem with the objective of minimizing transportation and stocking costs. A proactive warehouse selection method and an improved genetic algorithm are designed to obtain high-quality solutions within a reasonable computation time. Specifically， the method for selecting the categories and locations in proactive warehouses is based on commodity attributes and the spatiotemporal differentiation of customers. Additionally， to address the limitations of insufficient local search capabilities in traditional genetic algorithms， various neighborhood operations and 2-opt operator are incorporated， and the improved genetic algorithm is employed to solve the proposed problem. To validate the proposed model and algorithm in practical scenarios， cost and efficiency analyses are conducted for key category stocking， full-category stocking， and centralized stocking schemes. The computational results indicate that the full-category stocking scheme yields the highest stocking benefits. However， for categories with a smaller market share， the benefits of proactive stocking do not offset the associated stocking costs. Utilizing different vehicle types in the two-level network increases the system's adaptability to traffic conditions but also raises vehicle scheduling costs during the dynamic replenishment stage. Companies employing proactive stocking strategies should carefully select proactive categories and replenishment vehicle types in alignment with their business development to achieve a coordinated optimization of demand response and cost control. Finally， the study concludes that a distributed-based model considering product attributes and customer spatiotemporal characteristics can achieve a faster response to dynamic demands with lower delivery costs and higher efficiency. In practical operations， having more proactive categories is not always advantageous； the optimal number of proactive categories is determined by balancing customer response and cost control. Appropriate selection of proactive categories can effectively reduce operational costs， whereas inappropriate proactive stocking may lead to counterproductive results. Future research will consider incorporating real-time traffic information and disruption management to explore multi-category proactive management and route optimization under more complex scenarios.

Key words: dynamic vehicle routing problem, two-stage scheduling, proactive categories, improved genetic algorithm