To balance customer satisfaction across virtual and real-world interactions, we focus on enhancing service for dine-in customers at restaurants that typically prioritize online orders, such as those on Uber Eats. Utilizing three-agent scheduling strategies that adhere to each agent's specific requirements-by utilizing whether they are hard constraints or soft objectives-we effectively manage various types of orders, including immediate individual online orders, group reservations, and oral requests from dine-in customers. This approach significantly reduces waiting times and improves overall customer satisfaction. This study introduces a branch-and-bound algorithm with a tight lower bound based on preemption. Unique in its design, the lower bound aims to prioritize agents A and B and simultaneously reduce the total waiting time for agent C, representing dine-in customers. Computational experiments reveal that this lower bound can converge quickly. Compared with existing two-agent scheduling strategies, this lower bound can also be extended to other industries that require three or more different constraints or objectives, such as in the film and television industry where real actors, virtual avatars, and expensive 3D studios have distinct requirements. Multi-agent scheduling, Branch-and-bound algorithm, Lower bound, Waiting time
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