In this paper, multi-location path math model is established at the condition that the number of distribution centers, customers, and the service scope is known. Constraints are including customer demand, network matching, and vehicle loading. To solve the shortest path based on the maximum flow problem, the network model about one distribution center and six distribution customers is proposed and the solution is also given below. When the distribution of prices, vehicle specifications and node path are known, the optimal path is gotten according to check the model instance. So, it's feasible to solve the optimal path using the maximum flow.
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