Valuation of hospital resources: an optimization approach using clearing functions

We propose an approach to estimating the time-dependent marginal values of hospital resources facing heterogeneous patient demand over time using the dual variables of a novel dynamic patient admission and flow planning model maximizing hospital revenue. Clearing functions are used to represent the queuing behavior of the patients within the hospital. Using a large data set containing 17,483 patients treated over one year in a 400-bed hospital, we undertake a computational study where we derive the value of hospital resources under different demand and resource scenarios. Our results show that large instances of the model can be solved in reasonable CPU times, and that the model yields resource valuations that are qualitatively different from conventional approaches ignoring queueing costs.