## 1 Introduction  
Rapid advancements in artificial intelligence technology have facilitated the widespread integration of autonomous mobile robots (AMRs) into various domains, including industrial production [1] and medical rehabilitation. At smart hospitals, AMRs are employed to perform repetitive tasks, ensuring a safe distance between medical professionals and patients. This approach significantly mitigates the risk of personnel infection and enhances the overall safety of healthcare providers. Additionally, the utilization of AMRs in medical settings helps to alleviate the strain caused by staff shortages, thereby creating more value-added time for patient care [2]. This study is motivated by the specific requirements of Singapore Changi General Hospital, which intends to acquire a group of heterogeneous AMRs to improve medical services. The hospital has various routine medical requests, including tasks such as medication distribution, meal deliveries, and waste collection, which are intended to be handled by AMRs. Each type of medical request necessitates the use of a specific category of homogeneous AMRs. For instance, disinfection of wards requires different AMRs compared to those used for medication distribution. Consequently, the hospital needs to determine the optimal number of distinct AMR types to procure. It is essential to plan how these AMRs can deliver medical services effectively while adhering to multiple constraints [3]. The efficient and effective planning of service routes for AMRs is crucial for their operation. Scheduling optimization of AMRs is a type of research based on resource allocation that has gradually emerged in recent years. Previous studies have investigated various aspects of robot route planning. [PERSON] et al. [4] examined the sequencing problem of a single robot delivering parts to production lines, minimizing total travel time while adhering to time windows. Building upon this work, [PERSON] et al. [5] increased the capacity constraints during the service process. [PERSON] et al. [6] considered the physical constraint of battery levels and incorporated charging during driving in a single robot task planning problem. [PERSON] et al. [7] focused on scheduling and routing for AMR systems, aiming to minimize transportation request tardiness using a novel local search algorithm. All of the above literature assumes one robot performs only one route/trip. However, in practical applications, small vans are commonly used for package delivery due to their high mobility. In addition, drones and AMRs have the potential for delivering essential goods without direct human contact, but their limited capacity may require multiple trips [8]. To improve service efficiency, multiple robots can be arranged to make multiple trips. In recent years, there has been significant growth in research publications regarding robot scheduling problems that involve multiple trips. [PERSON] et al. [9; 10] address a mobile robot routing problem with multiple trips and time windows, emphasizing strict adherence to time windows at each stop. They proposed a two-index mixed integer programming model to solve this problem. [PERSON] et al. [11] investigated the scheduling of multiple mobile robots for multiple trips, aiming to minimize transportation and waiting costs. They employed a hybrid approach combining an improved genetic algorithm and tabu search algorithm to find optimal routes for the robots. Notably, [PERSON]. [9; 10; 11] did not consider electrical constraints in the context of robot scheduling problems. Moreover, these studies assume a deterministic environment, while the stochastic nature of driving and service times can significantly impact performance, as discussed in [12; 13]. This paper focuses on addressing these specific issues. This paper examines the scheduling strategy for autonomous mobile robots (AMRs), using drug delivery as a case study.