  Autonomous mobile robots (AMRs) play a crucial role in transportation and
service tasks at hospitals, contributing to enhanced efficiency and meeting
medical demands. This paper investigates the optimization problem of scheduling
strategies for AMRs at smart hospitals, where the service and travel times of
AMRs are stochastic. A stochastic mixed-integer programming model is formulated
to minimize the total cost of the hospital by reducing the number of AMRs and
travel distance while satisfying constraints such as AMR battery state of
charge, AMR capacity, and time windows for medical requests. To address this
objective, some properties of the solutions with time window constraints are
identified. The variable neighborhood search (VNS) algorithm is adjusted by
incorporating the properties of the AMR scheduling problem to solve the model.
Experimental results demonstrate that VNS generates high-quality solutions.
Both enhanced efficiency and the meeting of medical demands are achieved
through intelligently arranging the driving routes of AMRs for both charging
and service requests, resulting in substantial cost reductions for hospitals
and enhanced utilization of medical resources.
