With the constantly rising labor cost and deterioration in traffic congestion, the drone-based service emerges as a game changer for the urban last-mile delivery. Meanwhile, the human courier, as a traditional player in the last-mile delivery, appears as a typical form of gig economy, which is always available but with less revenue to harvest. To help the retailer with the fleet sizing decision-making, a co-sourcing mechanism is introduced, which is by nature a time-varying queue with a finite waiting space. And the orders are subject to cancellation when the waiting exceeds the customers’ patience time. Furthermore, three stochastic optimization models are formulated, namely, the pure stability, the pure profit, and the hybrid models, to jointly determine the optimal waiting space threshold and the drone fleet size, which are then approximated with fluid models. Based on the optimal control theory, the optimal decisions are obtained according to the outsourcing probability and time delay. As validated in the simulation, the proposed pure stability model can effectively stabilize the system performance at the control target, while the hybrid model takes into account both the stability and the profit. Finally, the tradeoff between profitability and volatility is analyzed, and the impacts of the parameters on the overall system performance are revealed.