Potential-Based Greedy Matching for Dynamic Delivery Pooling

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.