Optimal capacity planning for long-term care facilities considering patients’ gender, language, and age group
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".