Background: The intersection of artificial intelligence and OR offers a host of modeling, predictive, and adaptive analytical capabilities for complex healthcare, logistic, financial, and public administration systems. With the added complexity of these fields, in addition to traditional reporting systems, there is a growing demand for integrated analytical systems conducive to prediction, optimization, and adaptive learning.
Objective: The goal of this article is to develop a comprehensive academic framework for the conceptual and methodological foundations, main fields of application, implementation barriers, and research gaps of integrated decision support systems through the combination of statistical modeling, operations research, and intelligent systems.
Methods: A four-layered analytical framework was constructed comprising a layer for statistical modeling, an operations research layer, a layer for intelligent techniques, and a layer for Bayesian inference. Statistical modeling includes regression, generalized linear models, ARIMA time-series forecasting, and Bayesian inference. Operations research includes linear programming (LP), mixed-integer linear programming (MILP), and both dynamic and stochastic programming. Intelligent techniques include supervised learning, reinforcement learning, graph neural networks (GNNs), large language models (LLMs), and metaheuristics. In the tradition of the operations research methodological framework papers, an illustrative case study was created to show the logical and computational pipeline of the proposed framework using parameters from the literature. The case study focuses on hospital bed allocation and is intended to show the framework. It is not based on data that was collected from hospital visits. In the case study, forecasting ward demand was performed using a combination of multiple linear regression and an ARIMA (1,1,1)(1,0,1)₁₂ seasonal component. The predicted demand was used in an LP model to optimize demand fulfillment across the four clinical departments.
Results: The first integrated predictive-prescriptive framework reduced overall unmet bed demand from an estimated 14.7 % to 2.3 % using static historical allocation. This represents an 84% improvement in allocation efficiency. The hybrid ARIMA and regression model achieved a mean absolute percentage error (MAPE) of 8.6 %, a 22% improvement over the regression only baseline. A 15% variation in average length of stay (ALOS), an a 20 % emergency admission surge were simulated. The results confirmed the framework was robust.
Conclusion: Decision support systems enhanced by statistical forecasting integrated with LP-based systems outperform static allocation methods and remain interpretable. Advanced statistical methods bridge empirical data for optimization and sustain system reliability under uncertainty. Contextual variables such as calendar seasonality and epidemic phases improve forecasting in public health the most. End-to-end, predictive, and explainable AI systems integrated with equity constraints and hybrid stochastic AI systems will be most pertinent in future studies.