Optimal capacity planning for long-term care facilities considering patients' gender, language, and age group

Long-term care facility networks in Canada face significant challenges in balancing demand and capacity, a problem exacerbated by rising demand. In other words, the growing elderly population is escalating the need for long-term care resources. To address this issue, this study proposes a Mixed-Integer Linear Programming model based on the current standing of the long-term care system in Ontario, a representative case for considering varied patient supports. The proposed model simultaneously optimizes the timing and location of constructing new long-term care facilities while dynamically adjusting each facility's capacity, including human resources and beds. Moreover, patient assignments are optimized based on their demand region, gender, language, and age group over a finite time horizon. The model incorporates multiple constraints to accommodate patients' gender and language, addressing language barriers, alleviating feelings of loneliness, and aligning with Canada's commitment to inclusive care. Additionally, it considers patient journeys by incorporating age groups and assigning patients from different demand regions in an equitable manner through the geographical equity constraint. To validate our proposed model, we conduct a case study on the existing network in Hamilton, Ontario. An extensive set of numerical analyses is executed to provide insights into the problem. Most importantly, the results demonstrate that the model effectively optimizes facility placement and patient allocation while significantly reducing un-assignment and misassignment rates. Specifically, the results indicate that over 88% of patient demand can be accommodated annually throughout a five-year planning horizon. In addition, patients can be assigned based on language and gender with marginal additional costs. Lastly, operational costs constitute the largest share of total expenditures, whereas misassignment costs account for the smallest proportion.