Robot delivery studies can overstate transport capacity when travel to pickups and human support fall outside the modeled schedule. We formulate a location aware dispatch model that couples robot admission to transporter support and shared elevators, charging, and cleaning. The model replays 33,079 observed hospital requests; missing contents, deadlines, staffing, and completion times remain explicit scenario assumptions. Two full grids compare human dispatch, a resource aware controller, and a proximity and workload benchmark in 30 paired replications per scenario. An exploratory extension tests a simpler deadline admission rule under the same operating model. Pickup travel increases demand on a pooled elevator bank. In one high staffing case, raising assumed elevator capacity from two to four reduces human only lateness from 55.11\% to 3.18\%, exceeding the dispatch differences. Direct policy comparisons and robot coverage distinguish admission selectivity from system service. The analysis explains why a robot can pass a deadline admission test yet delay service through staff handoffs and shared facilities. Its contribution is a reproducible evaluation of coupled dispatch workflows, with a clear separation between admission, completion, and return to availability. The results are conditional comparisons, not estimates of hospital benefit or released clinical capacity.

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