Consistent home health care routing and scheduling problem under time uncertainty
Bibliographic record
Abstract
• We tackle consistent home health care routing under travel and service time uncertainty. • Scenario-based and extreme value theory-based (EVT) stochastic models are introduced. • We propose a decomposition algorithm that effectively handles nonlinear constraints in EVT-based model. • We comprehensively demonstrate the value of the stochastic models against the model in the literature. This study addresses the challenge of routing and scheduling care workers for home health care logistics in a stochastic environment, where consistency in service delivery is crucial. The primary research question focuses on determining reliable schedules while ensuring timely care despite the uncertainty of travel and service times (TST). The objective is to maximize the number of new patients care workers can attend to while ensuring feasible and consistent schedules. To tackle this challenge, we propose a chance-constrained optimization modeling framework that ensures a likelihood of on-time arrivals, with arrival time distributions at patients estimated empirically and analytically via a discrete scenario set and an extreme value theory-based (EVT-based) approach, respectively. The EVT-based approximation incorporates nonlinear constraints that link patient visit times with the probability of on-time arrivals. The problem is decomposed into a master problem, which optimizes patient assignments, and subproblems, which generate feasible schedules and routes. To solve this problem, we propose a branch-and-check (B&Ch) algorithm, where the subproblems are solved efficiently via constraint programming. Computational results demonstrate that our solution approach, particularly with the EVT-based approximation, can efficiently handle practical benchmark instances while producing schedules with significantly higher service levels than the deterministic model in the literature.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| 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".