Courier assignment in meal delivery via integer programming: A case study in Rome

We present an optimization model for assigning orders to couriers developed for an Italian meal delivery firm focusing on Rome. The firm focuses on top-end restaurants and customers and pursues high Quality of Service through careful management of delays. Our model reflects that in the firm's business, the majority of orders are placed in advance. This took us to design a sequential decision process implementing a rolling horizon approach where we do not try to anticipate future demands. We, therefore, iterate the solution of a fully deterministic optimization problem, the {\em Offline Couriers Assignment Problem} (ocap), where we assume full knowledge} of the orders and aim at minimizing delays and rejections. We solve ocap through integer linear programming and in particular by a ``flow-like'' formulation on a suitable network whose size is kept as small as possible. We validate both the quality of this formulation and the sequential decision process through some computational tests on real instances collected on the ground. We make these instances available to the scientific community.