We study the 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 other 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 length of each job as its opportunity cost, via a potential-based greedy algorithm (PB). The algorithm is very simple, pooling each departing job with the available job that maximizes the savings in travel distance minus a half of its distance (i.e. the potential). On the theoretical front, we show that PB significantly improves upon a naive greedy algorithm in terms of worst-case performance: as the density of the market increases, the regret per job vanishes under PB but remains constant under naive greedy. In addition, we show that the potential approximates the marginal cost of dispatching each job in a stochastic setting with sufficient density. Moreover, we conduct extensive numerical experiments and show that despite its simplicity, PB consistently outperforms a number of benchmark algorithms, including (i) batching-based heuristics that are widely used in practice, and (ii) forecast-aware heuristics that estimate the marginal costs of dispatching different jobs using historical data.

翻译：本文研究将多个订单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。当订单需要派发时，平台必须决定将其与哪些（若有）其他可用订单进行拼单，这需要权衡即时效率提升与保留各订单以等待未来拼单机会的不确定差异收益。本文通过基于势能的贪心算法（PB）证明了使用各任务长度作为机会成本的有效性。该算法极为简洁：将每个出发任务与可用任务进行匹配，以最大化行程距离的节省量减去其距离的一半（即势能）。在理论层面，我们证明PB在极端情况性能上显著优于朴素贪心算法：随着市场密度的增加，PB算法下每任务的遗憾值趋近于零，而朴素贪心算法下则保持恒定。此外，我们证明在具有足够密度的随机场景中，该势能可近似表示派发各任务的边际成本。进一步，我们开展了大量数值实验，结果表明尽管算法简单，PB始终优于多种基准算法，包括：（i）实践中广泛使用的基于批处理的启发式算法，以及（ii）利用历史数据估计派发不同任务边际成本的预测感知启发式算法。