Online restaurant aggregators have experienced significant sales growth in recent years, driving demand for meal delivery in the US. Meal delivery logistics is quite challenging, primarily due to the difficulty in managing the supply of delivery resources to satisfy dynamic and uncertain customer demand under very tight time constraints. In this paper, we study several questions in meal delivery operations focused on matching the correct levels of supply with demand. To ensure excellent customer service, delivery aggregators may, for example, decide to temporarily decrease demand during an operating day by temporarily reducing the delivery area for one or more restaurants. We show that such simple demand restriction strategies allow a significantly smaller fleet to meet service requirements. To simplify the analysis, we focus on problem geometries that enable the use of stylized mixed-integer programs to optimally deploy a fleet of couriers serving large numbers of orders. Applying the proposed framework to several scenarios with one and two depots, we conduct an extensive experimental study of the effects on system performance of (i) allowing courier sharing between multiple depots, (ii) relaxing the delivery deadlines of placed orders, and (iii) restricting demand through limited adjustment of the coverage of restaurants. The results demonstrate the potential effectiveness of different dispatch control and demand management mechanisms, in terms of both the required courier fleet size to serve requests and the coverage level of orders.