Optimizing Equity in Healthcare Access: An Integer Programming Approach to Emergency Department Closures and Travel Burden Disparities in Ontario
Bibliographic record
Abstract
Emergency department (ED) closures in Ontario disproportionately affect rural communities. Patients in rural areas already face inequitable access to care, with many lacking a primary care provider. In many communities, the ED serves as both emergency and primary care. When an ED closes, local patients must still seek care, often traveling long distances to the next closest ED. This extra travel burden varies across Ontario, making ED closures have a disproportionate impact on rural communities in terms of travel burden. This thesis addresses these disparities by filling the gap in ED closure research and proposing an optimization framework as a solution. First, it examines the travel burden caused by closures and the resulting disparities in access between Northern and Southern Ontario. Data on ED closures from January 2022 to December 2024 were gathered from public sources. A network analysis mapped populations at the dissemination area (DA) level to the nearest EDs using the Google Maps API. Travel times to specialized services including computed tomography, magnetic resonance imaging, acute stroke thrombolysis centres, endovascular therapy centres, and intensive care units were also calculated. For historical closure data, travel burden for the closest DAs was calculated. A simulation then hypothetically closed all rural EDs one at a time, calculating the resulting travel burden. To compare regional disparities, closures in Northern and Southern Ontario were analyzed for both historical and simulated data. Post-closure travel burdens were also assessed across dimensions of the Ontario Marginalization Index. Second, this thesis introduces a framework for planning ED closures that minimizes travel burdens while balancing operational constraints. Two Integer Linear Programming (ILP) models were developed within this framework. The Capacitated p-Median Problem (CpMP) model identifies closures that minimize patient travel times, with results aligning to some historical closures (e.g., Durham Memorial and Chesley District), reflecting sensitivity to factors such as ED proximity and urban service density. The new Temporal Geo-constrained CpMP (TG-CpMP) extends this with multi-period planning and geographic equity mechanisms. Compared to ad hoc closures, TG-CpMP reduced affected DAs by 35–76% and lowered maximum travel times.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".