We investigate some optimization models for meal delivery that stem from a collaboration with an Italian company mainly operating in Rome. The focus of this company is on top-end customers, and the company pursues high Quality of Service through a careful management of delays. We then design optimization models and algorithms for dispatching orders to couriers to avoid as much as possible delays and cancellations. The solution approach is based on the iterative solution of fully deterministic optimization sub-problems that are solved through integer programs exploiting a suitable "floow-like" formulation. We validate both the approach and the integer programming formulation through some computational tests on some real instances collected on the ground during our collaboration. We make these instances available to the scientific community and discuss a few insights on the meal delivery market in the area of Rome that may be of interest to other research groups.