The uncertainty of logistics distribution demands leads to fluctuations in logistics delivery costs, which increases the difficulty of logistics management and exacerbates the inefficiency of the "last mile" delivery. Aiming to reduce the costs and shorten the delivery time of last-mile logistics, a multi-objective optimization strategy based on a "0-1" integer programming model was proposed, considering the transportation capacity and population density of the service area under uncertain package volumes. A dynamic location model for logistics distribution centers was established and validated through simulation using Anylogic. The results of the study indicate that, in the case of significant short-term fluctuations in the number of packages to be delivered, differentiated adjustments in the level of transportation capacity, outlet locations, and service capabilities are necessary to achieve cost reduction and efficiency enhancement.