  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.
