An effective examination and test schedule for patients plays a crucial role in hospital resource management. In this work, we formulate a new reactive patient-flow scheduling problem in multi-department hospitals where walk-in patients arrive over time and each patient requires multiple examinations per visit. Upon each arrival, the scheduler computes a feasible examination pathway-both the sequence of examinations and the room assignment-for the incoming patient only, while previously scheduled assignments remain fixed. This process is subject to medical precedence constraints and room capacity limitations. We model the problem declaratively in Answer Set Programming (ASP) with clingo, and optimize a two-part cost: travel time between consecutive examination locations and queue-induced waiting time, weighted by the duration of the upcoming examination. To assess robustness under stochastic service times, we propose a Discrete-Event Simulation (DES) evaluation layer and a baseline greedy policy for comparison. On large-scale synthetic datasets across various capacity regimes and patient loads, the ASP approach reduces median stay time and increases the proportion of zero-wait patients compared to DES-based baselines. These improvements are most pronounced under heavy load, while the approach still outperforms baselines across all capacity settings, with smaller gains at higher capacities.

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