Given a stream of food orders and available delivery vehicles, how should orders be assigned to vehicles so that the delivery time is minimized? Several decisions have to be made: (1) assignment of orders to vehicles, (2) grouping orders into batches to cope with limited vehicle availability, and (3) adapting to dynamic positions of delivery vehicles. We show that the minimization problem is not only NP-hard but inapproximable in polynomial time. To mitigate this computational bottleneck, we develop an algorithm called FoodMatch, which maps the vehicle assignment problem to that of minimum weight perfect matching on a bipartite graph. To further reduce the quadratic construction cost of the bipartite graph, we deploy best-first search to only compute a subgraph that is highly likely to contain the minimum matching. The solution quality is further enhanced by reducing batching to a graph clustering problem and anticipating dynamic positions of vehicles through angular distance. Extensive experiments on food-delivery data from large metropolitan cities establish that FoodMatch is substantially better than baseline strategies on a number of metrics, while being efficient enough to handle real-world workloads.
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