We study the dynamic pooling of multiple orders into a single trip, a strategy widely adopted by online delivery platforms. When an order has to be dispatched, the platform must determine which (if any) of the available orders to pool it with, weighing the immediate efficiency gains against the uncertain, differential benefits of holding each order for future pooling opportunities. In this paper, we demonstrate the effectiveness of using the delivery distance as a proxy for opportunity cost via a potential-based greedy algorithm (PB). The algorithm is simple, pooling each departing job with the available job that maximizes the immediate savings in travel distance minus "half its delivery distance", which we call the potential of the available job. Theoretically, we show that PB achieves vanishing worst-case regret per job as market density increases, whereas a naive greedy policy suffers constant regret. We further show that the potential approximates the true opportunity cost of dispatching a job, in a stochastic setting with sufficient density. Finally, we conduct extensive numerical experiments on both synthetic data and real-world data from the Meituan platform. Despite being forecast-agnostic, PB consistently outperforms greedy heuristics that rely on historical data. Moreover, PB achieves performance comparable to computationally-intensive batching heuristics, which themselves also benefit from incorporating the potential to further improve their performance or drastically reduce computational costs.

翻译：本文研究将多个订单动态合并为单次配送的策略，该策略已被在线配送平台广泛采用。当订单需要调度时，平台必须决定将其与哪个（若有）可用订单进行合并，这需要权衡即时效率提升与保留每个订单以等待未来合并机会所带来的不确定、差异化收益。本文通过基于势能的贪心算法（PB）证明了使用配送距离作为机会成本代理变量的有效性。该算法简洁明了：将每个出发订单与能最大化即时行程节省距离减去"其配送距离的一半"（我们称之为该可用订单的势能）的可用订单进行合并。理论上，我们证明随着市场密度的增加，PB算法实现了每订单最坏情况遗憾的渐近消失，而朴素贪心策略则存在恒定遗憾。我们进一步证明，在具有足够密度的随机场景中，势能函数可近似表示调度订单的真实机会成本。最后，我们在合成数据和美团平台真实数据上进行了大量数值实验。尽管无需预测信息，PB算法始终优于依赖历史数据的贪心启发式算法。此外，PB实现了与计算密集型批处理启发式算法相当的性能，而后者本身也能通过引入势能函数来进一步提升性能或显著降低计算成本。