A min-max theorem for the minimum fleet-size problem

11/21/2022

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by   Tinghan Ye, et al.

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A retrospective fleet-sizing problem can be solved via bipartite matching, where a maximum cardinality matching corresponds to the minimum number of vehicles needed to cover all trips. We prove a min-max theorem on this minimum fleet-size problem: the maximum number of pairwise incompatible trips is equal to the minimum fleet size needed.