The on-demand delivery platforms for food and grocery have grown rapidly. One claimed benefit of those platforms is the potential to optimize courier routing by sharing couriers among many vendors, such as restaurants or grocery stores. However, it is puzzling to observe that the largest food-delivery platforms do allow restaurants to employ their own delivery units. To study whether and how courier sharing contributes to the reduction of delivery costs, we consider a spatial queuing model in which couriers are servers, and it takes a different amount of traveling time to serve customers depending on their vendor of choice, their own location, and the dispatch policy. Surprisingly, we find that in many cases, the dedicated policy can outperform the sharing one. This result is attributed to the random imbalance and randomness in the courtier allocation that sharing creates. Under the growth target strategy of achieving an exogenous demand rate, if the market is sufficiently large, the sharing policy achieves a higher profit than the dedicated one, and otherwise, if the market is small, the dedicated policy is more profitable. However, under the profit maximization strategy of endogenizing the demand rate, we find that it is even more likely the dedicated policy is optimal: in addition to a market size condition, a high enough service value is required for the sharing policy to be optimal. This is because, under profit maximization, the platform may want to increase the delivery fee and force out distant customers, which eliminates the benefit of courier sharing. In addition, we show that in those markets where restaurants have a more distinctive cuisine, the sharing policy tends to do better, and otherwise, in those markets with similar restaurants, the dedicated policy has an edge. Lastly, we extend the results from the base model to account for multiple couriers and impatient customers
