<p>The applications of drones for improving meal delivery efficiency are increasingly drawing attention. This paper examines a meal delivery routing problem (MDRP), where a parallel drone-courier cooperative system is developed to serve dynamic demands from customers with heterogeneous time sensitivity. We formulate the problem as a bi-objective mathematical model aiming at maximizing customer satisfaction while minimizing the operational cost. To address the dynamic problem, it is segmented into several static subproblems using the rolling horizon approach, which are solved in chronological order. For each static subproblem, a hybrid discrete multi-objective gray wolf optimizer (HDMOGWO) algorithm is proposed to generate high-quality solutions. The algorithm integrates the modified prey search and adaptive large neighborhood search (ALNS) to enhance global and local search capability, respectively. We verify the performance of the algorithm through numerical experiments and a case study in the real world and derive managerial insights from sensitivity analysis. Notably, the results of the case study indicate that, compared with the courier-only mode, the proposed drone-courier cooperative system increases customer satisfaction by 19.27%, reduces operational costs by 109.36%, and decreases average delivery time by 24.93%.</p>