Food-Delivery Platforms : A Near-Optimal Policy for Capacity Sizing, Order Batching, and Spatial Routing

We study an infinite-horizon, stochastic, dynamic optimization problem for an on-demand food-delivery platform, with a one-time capacity-investment decision on the number of capacitated drivers to employ at the beginning of the horizon, and real-time order-batching and driver-routing decisions for the spatial delivery of orders. The objective is to minimize the long-run average cost incurred per unit time, where the cost includes the wages of the drivers and the waiting costs of the orders. We first characterize the fundamental trade-off between balancing drivers' salary and customers' waiting times for spatial delivery, and leverage this relationship to establish a lower bound on the cost under any policy for the platform. We then identify a simple region-partitioning algorithm whose gap with respect to this lower bound vanishes in a meaningful asymptotic regime. Together, our results establish the optimality of a safety-staffing rule with a safety level that is proportional to the nominal load to the power of 2/3, where the nominal load is the minimum number of drivers needed to avoid the system from exploding. This echoes a similar finding for a spatial ride-hailing platform reported in Besbes et al. (2021) and represents a fundamental departure from the square-root safety-staffing rule for capacity sizing in conventional service systems without the spatial feature