AI-enhanced robust method for integrated healthcare resource pre-positioning and patient scheduling

This paper aims to optimise healthcare resource pre-positioning, patient scheduling, and patient transferring under uncertain demands and stochastic resource consumption. We propose a two-stage stochastic programming model that formulates the patient scheduling problem as a Markov decision process. To address complexities and uncertainties, we use Artificial Intelligence (AI) techniques to improve both model formulation and algorithmic performance. To tackle the limited data challenge, we introduce a Wasserstein distance-based ambiguity set and propose a two-stage distributionally robust optimisation (DRO) model, which derives a deterministic equivalent using the Lagrangian dual of non-anticipativity constraints. The solution process is accelerated with a scenario decomposition approach and the K-means clustering method. Both theoretical and numerical results demonstrate the consistency of the two-stage DRO model with the sample average approximation (SAA) method. The potential of AI to improve the model's performance is evident through the significant reduction in computation time achieved with the K-means clustering approach without compromising solution quality. Compared to the SAA method, the DRO model exhibits a considerable reduction in the waiting penalty cost for out-of-sample cases, ranging from $ 43.06\% $ 43.06% to $ 81.23\% $ 81.23%. Numerical results show that the proposed algorithm outperforms SAA methods and several benchmark policies in terms of computational efficiency and solutions.