Data-driven distributionally robust vehicle balancing using dynamic region partitions.

With the transformation to smarter cities and the development of technologies, a large amount of data is collected from sensors in real-time. This paradigm provides opportunities for improving transportation systems' performance by allocating vehicles towards mobility predicted demand proactively. However, how to deal with uncertainties in demand probability distribution for improving the average system performance is still a challenging and unsolved task. Considering this problem, in this work, we develop a data-driven distributionally robust vehicle balancing method to minimize the worst-case expected cost. We design an efficient algorithm for constructing uncertainty sets of random demand probability distributions, and leverage a quad-tree dynamic region partition method for better capturing the dynamic spatial-temporal properties of the uncertain demand. We then prove equivalent computationally tractable form for numerically solving the distributionally robust problem. We evaluate the performance of the data-driven vehicle balancing framework based on four years of taxi trip data for New York City. We show that the average total idle driving distance is reduced by 30% with the distributionally robust vehicle balancing method using quad-tree dynamic region partition method, compared with vehicle balancing solutions based on static region partitions without considering demand uncertainties. This is about 60 million miles or 8 million dollars cost reduction annually in NYC.