Predictive and prescriptive analytics for multi-site modelling of frail and elderly patient services

TL;DR

The paper tackles hospital bed and staffing optimization for frail and elderly patients by integrating CART-based LOS predictions with deterministic and two-stage stochastic programming across a network of 11 UK hospitals. By using CART to generate demand inputs and combining them with multi-site optimization, the study demonstrates robust planning under uncertainty and reports a ~7% cost reduction over average-based approaches, with additional gains from incorporating patient-specific LOS. Key contributions include linking predictive LOS groupings to prescriptive resource allocation, evaluating value of stochastic solutions, and showing superior performance of stochastic and CART-linked approaches over deterministic averages. The approach advances healthcare operations by offering interpretable, data-driven segmentation coupled with robust, regionally distributed resource planning, applicable to other sectors facing similar demand variability. Overall, the work provides a practical framework for robust capacity planning in elderly care, with clear managerial implications and avenues for future enhancement such as online optimization and causal analyses.

Abstract

Many economies are challenged by the effects of an ageing population, particularly in sectors where resource capacity planning is critical, such as healthcare. This research addresses the operational challenges of bed and staffing capacity planning in hospital wards by using predictive and prescriptive analytical methods, both individually and in tandem. We applied these methodologies to a study of 165,000 patients across a network of 11 hospitals in the UK. Predictive modelling, specifically Classification and Regression Trees, forecasts patient length of stay based on clinical and demographic data. On the prescriptive side, deterministic and two-stage stochastic optimisation models determine optimal bed and staff planning strategies to minimise costs. Linking the predictive models with the prescriptive optimisation models, generates demand forecasts that inform the optimisation process, providing accurate and practical solutions. The results demonstrate that this integrated approach captures real-world variations in patient LOS and offers a 7% cost saving compared to average-based planning. This approach helps healthcare managers make robust decisions by incorporating patient-specific characteristics, improving capacity allocation, and mitigating risks associated with demand variability. Consequently, this combined methodology can be broadly extended across various sectors facing similar challenges, showcasing the versatility and effectiveness of integrating predictive and prescriptive analytics.

Figures (2)

• Figure 1: Heatmap of bed locations for each specialty within each hospital for the deterministic model.
• Figure 2: Heatmap of bed locations for each specialty within each hospital for the two-stage stochastic model.