How to dynamically measure the local-to-global spatio-temporal coherence between demand and supply networks is a fundamental task for ride-sourcing platforms, such as DiDi. Such coherence measurement is critically important for the quantification of the market efficiency and the comparison of different platform policies, such as dispatching. The aim of this paper is to introduce a graph-based equilibrium metric (GEM) to quantify the distance between demand and supply networks based on a weighted graph structure. We formulate GEM as the optimal objective value of an unbalanced transport problem, which can be efficiently solved by optimizing an equivalent linear programming. We examine how the GEM can help solve three operational tasks of ride-sourcing platforms. The first one is that GEM achieves up to 70.6% reduction in root-mean-square error over the second-best distance measurement for the prediction accuracy. The second one is that the use of GEM for designing order dispatching policy increases answer rate and drivers revenue for more than 1%, representing a huge improvement in number. The third one is that GEM is to serve as an endpoint for comparing different platform policies in AB test.
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