This paper investigates the optimization problem of scheduling autonomous mobile robots (AMRs) in hospital settings, considering dynamic requests with different priorities. The primary objective is to minimize the daily service cost by dynamically planning routes for the limited number of available AMRs. The total cost consists of AMR's purchase cost, transportation cost, delay penalty cost, and loss of denial of service. To address this problem, we have established a two-stage mathematical programming model. In the first stage, a tabu search algorithm is employed to plan prior routes for all known medical requests. The second stage involves planning for real-time received dynamic requests using the efficient insertion algorithm with decision rules, which enables quick response based on the time window and demand constraints of the dynamic requests. One of the main contributions of this study is to make resource allocation decisions based on the present number of service AMRs for dynamic requests with different priorities. Computational experiments using Lackner instances demonstrate the efficient insertion algorithm with decision rules is very fast and robust in solving the dynamic AMR routing problem with time windows and request priority. Additionally, we provide managerial insights concerning the AMR's safety stock settings, which can aid in decision-making processes.

翻译：本文研究了医院环境下考虑不同优先级动态请求的自主移动机器人（AMR）调度优化问题。主要目标是通过动态规划有限数量可用AMR的路径，最小化每日服务成本。总成本由AMR的购置成本、运输成本、延迟惩罚成本和拒绝服务损失组成。针对该问题，我们建立了一个两阶段数学规划模型。在第一阶段，采用禁忌搜索算法为所有已知医疗请求规划先验路径；第二阶段则利用带有决策规则的高效插入算法处理实时接收的动态请求，该算法能够基于动态请求的时间窗和需求约束实现快速响应。本研究的主要贡献之一是针对不同优先级的动态请求，根据当前服务AMR数量进行资源分配决策。基于Lackner实例的计算实验表明，带决策规则的高效插入算法在求解具有时间窗和请求优先级的动态AMR路径问题时具有极快的求解速度和鲁棒性。此外，我们还提出了关于AMR安全库存设置的启示性管理见解，可为决策过程提供支持。