Optimizing hospital length of stay and bed allocation using a fuzzy stochastic transportation problem framework with lomax distribution.

Managing hospital Length of Stay (LOS) is essential for improving patient flow and resource utilization. This study introduces the Fuzzy Stochastic Transportation Problem with Lomax Distribution (FSTPWLD) as a framework to address LOS variability. The Lomax distribution effectively represents heavy-tailed data, capturing the uncertainty and skewness typical of patient discharge times. By integrating this distribution into the FSTPWLD model, the study offers a novel method to predict and manage LOS under fluctuating demand and capacity. The model aims to minimize operational costs while maintaining high standards of patient care, using probabilistic constraints and objective functions. Numerical experiments and simulations demonstrate the effectiveness of our approach in improving resource allocation and reducing bottlenecks. The results highlight the potential of using advanced probabilistic models to enhance decision-making processes in healthcare management, providing a foundation for future research and practical applications in hospital administration. The model demonstrated its efficacy with a predicted New Average Length of Stay (New ALOS) achieving a mean absolute error (MAE) of ±5 ., significantly improving accuracy compared to traditional methods. Additionally, the integration of fuzzy and stochastic elements led to a 20 . reduction in bed allocation mismatches, optimizing resource utilization across hospital departments.•Novel Integration of Lomax Distribution in FSTPWLD: Utilizes the Lomax distribution to model heavy-tailed LOS data, capturing inherent uncertainty and variability in hospital discharge times.•Optimized Decision-Making for Healthcare Management: Employs probabilistic constraints and fuzzy stochastic models to balance operational costs and patient care quality, improving resource allocation.•Validated through Simulations and Practical Scenarios: Numerical experiments highlight the model's effectiveness in reducing bottlenecks and enhancing hospital administration efficiency.