Metamodel-based simulation optimisation for bed allocation

Hospital beds are one of the most critical resources in healthcare institutions. In practice, beds are usually allocated to different departments in advance to accommodate different kinds of patients. Inappropriate decisions in the allocation may lead to the idleness of beds or the high rejection ratio of patients. Hospital managers are under pressure to allocate beds to different departments. High variability in patient arrivals and service times make the allocation problem complex and challenging to solve. To address this problem, a mixed-integer non-linear programming model is formulated, with the objective of minimising the weighted cost of rejecting patients and holding them waiting. To solve this model, a data-driven metamodel simulation optimisation method is proposed, in which metamodels, based on an analytical queuing model and a general function, are proposed and embedded into a general-purpose algorithm Adaptive Hyperbox Algorithm. The metamodels designated for local and global approximation are separately fitted using different sets of simulation observations, which can combine structural information and simulation information, and can provide insightful guidance in solution improvements. A case study is conducted based on the real data collected from a public hospital in Shanghai. Numerical results demonstrate the efficiency of the proposed method.