Allocation‐routing problem in a multi‐hospital home hospitalization system: the case of a healthcare provider in Portugal

Abstract Home hospitalization (HH) represents a paradigm shift in healthcare delivery, providing vital patient‐centered services that enhance care quality and significantly reduce the burden on conventional healthcare facilities. Given the complexity of HH systems, where specialized nurses and doctors allocate their time between inpatient and outpatient systems, efficiently managing their time and workload becomes critical. For this purpose, we develop the multi‐hospital home hospitalization allocation‐routing problem as a mixed‐integer linear programming formulation. We define three different objective functions: minimizing routing costs, workload balancing among nurses, and the minimization of employed doctors. The model is solved by optimizing each objective function individually and then analyzing the trade‐offs by combining the functions in pairs, generating a series of two‐objective Pareto frontiers as part of a comprehensive multi‐objective framework. The model is validated using benchmark instances derived from HH historical data. Through a single‐objective perspective, we provide an economic analysis that assesses the cost implications and the benefits of opening new HH units. Furthermore, the bi‐objective results are analyzed presenting Pareto frontiers to facilitate the provider's decision‐making process regarding the trade‐offs between different objectives. A technique for order of preference by similarity to ideal solution (TOPSIS) analysis is subsequently applied to identify the most promising solution according to varying objectives weights. Finally, useful managerial insights are developed to assess the impact of prioritizing one objective function over the other and the economi implications on different strategic options.