Integrated treatment scheduling and logistics planning for a hemodialysis center after a disaster with robust travel times

Hemodialysis centers use session-based scheduling to provide regular treatments for chronic hemodialysis patients. Optimizing the use of hemodialysis machines is crucial to managing daily patient loads, which requires the timely initiation of parallel sessions. Many centers offer transportation (shuttle) services to ensure punctual patient arrivals. However, post-disaster scenarios pose significant challenges, including road network disruptions, heightened demand for hemodialysis services, and reduced service capacity. The provision of shortened hemodialysis treatments in disaster conditions further complicates planning. This study addresses patient transportation and treatment scheduling in a hemodialysis center following a disaster, accounting for travel time uncertainties due to road disruptions. For a cohort of chronic hemodialysis patients requiring periodic treatment over a defined relief planning horizon (e.g., two weeks) and with constrained session capacity, the center must determine which patients to serve each day and each session with what type of treatments (regular or short) and construct shuttle routes. We introduce an integer programming model to address this integrated treatment scheduling and routing problem. We incorporate uncertainties in travel times in a post-disaster setting by a data driven robust optimization approach. Additionally, we develop an efficient decomposition-based constructive heuristic and matheuristic to solve the resulting problem. We illustrate our approach on a case study based on an earthquake scenario in Istanbul, utilizing data from the Istanbul Metropolitan Municipality to map road closures.