Maximum Flow Model With Multiple Origin and Destination and Its Application in Designing Urban Drainage Systems

Abstract

In this paper, a multi-origin and multi-destination maximum flow model is proposed by integrating the objective programming method with graph theory. Through Model 1, low-cost design of drainage pipeline networks can be achieved. For instance, in the experiments, certain pipelines such as Pipeline 9, Pipeline 20, and Pipeline 27 can be excluded during the initial construction phase while still maintaining effective drainage performance and reducing costs. Model 2 enables the monitoring of drainage capacity at various nodes within the existing drainage system. For example, under a specific rainfall intensity, it was observed that certain nodes, such as Nodes 9~16, Node 45, and Node 48, exhibit poor drainage capacity, necessitating precautionary measures. Model 3 focuses on the expansion planning of the drainage system, ensuring its normal operation under certain rainfall intensities. The results based on a specific area in Changchun City demonstrate that the proposed models not only possess strong practical application value in the design of urban drainage systems but also have broader applicability in other fields such as traffic flow and logistics supply chain planning. This study opens up new avenues for model construction and enriches the practical application effects of mixed-integer programming models.