Hospital delivery robots stop competing for the same job: hierarchical policy cuts weighted tardiness from 2359 to 29 and lifts STAT on-time rate to 0.969

Scheduling hospital delivery robots no longer means dispatching one job at a time under a single queueing rule; the choice of which request to serve and the order of stops are decided in one policy, and the shared elevator bottleneck is brought into the decision loop. Prior dispatching rules rank priority but plan no routes, metaheuristics plan routes but run offline, and learned routers usually optimize a single objective and rarely bound the tail of clinical delay. In a discrete-event simulation of a four-floor hospital with 32 service points and three elevators, one reserved as an express car, the heavy-load setting uses twelve robots, 1.80 requests per minute, an eight-hour shift and twenty paired seeds; HMART-H beats the compared dispatching rules, metaheuristics and two learning baselines on total weighted tardiness, work-in-process, makespan, throughput, travel distance and STAT on-time rate.

The system has three parts: a shared graph-attention encoder reads all robots and open requests, a sequential assignment decoder picks a request for each robot in turn, and a route-improvement decoder reorders stops. The assignment decoder decides robot by robot, and each robot sees only the choices already made by earlier robots, so two robots do not claim the same STAT item; a model predictive control layer solves speed and hold actions for the elevators over a short horizon. At the heavy load of twelve robots and 1.80 requests per minute over twenty paired seeds, HMART-H reaches a mean total weighted tardiness of 29±6, work-in-process of 14.3±1.9, STAT on-time rate of 0.969±0.007 and a 95th-percentile conditional value-at-risk of per-request weighted tardiness of 0.70±0.14.

Replacing the assignment decoder with a trained attention network still lets the policy run on an unseen larger fleet and on different building layouts without retraining. The engineered decoder is stronger on the demand mix it was tuned for, but that advantage depends on constants tuned to that mix and reverses once the mix shifts. HMART-RL is trained with eight robots at a stable load and reaches 40±8 total weighted tardiness and a 0.965±0.008 STAT on-time rate on the unseen twelve-robot heavy-load setting; when the STAT share rises from 10% to 25%, HMART-H degrades to 268±41 while HMART-RL reaches 96±19.

All results come from a discrete-event simulator of one four-floor building with 32 service points and three elevators; the heavy-load main comparison uses twelve robots, 1.80 requests per minute, an eight-hour shift and twenty paired seeds, and the authors state that these gains require confirmation in a live building and list a field study as the next step.

The authors note that the static exact model absorbs elevator contention into arc travel times, so the reported optimality gaps are understated for every method including HMART; the learned component covers only the assignment decoder, while route improvement and elevator coordination remain engineered, so the complete end-to-end architecture is not evaluated; the stability statement is a drift argument for a work-conserving policy rather than a proof for the learned policy; and demand is modelled as independent Poisson streams by class, which does not reproduce ward-round structure or daily patterns.