A Constraint Satisfaction Problem (CSP) Approach for the Nurse Scheduling Problem
Bibliographic record
Abstract
The Nurse Scheduling Problem (NSP) is a well-known NP-hard combinatorial optimization problem. Solving the NSP involves assigning feasible shift patterns to nurses, satisfying hard constraints while optimizing objectives such as penalty costs. Various approaches have been proposed to tackle the NSP, explicitly using exact or approximate methods, or implicitly using machine learning models. Exact techniques, e.g., Mixed-Integer Linear Programming (MILP), are often time-consuming while approximation methods such as metaheuristics trade running time for the quality of the solution returned. In this paper, we propose an exact alternative method to model and solve the NSP using the Constraint Satisfaction Problem (CSP) framework. More precisely, we use the Weighted Constraint Satisfaction Problem (WCSP) to capture all the constraints related to working requirements, in addition to the quantified nurses' preferences (represented as weights) over shift patterns. Solving the WCSP (corresponding to a given NSP instance) consists of finding an optimal solution satisfying all the constraints while optimizing the objective function (total weight). To solve the WCSP, we have adopted a variant of the Branch & Bound (B&B) algorithm, enhanced with constraint propagation and variables/values ordering heuristics. To assess the time efficiency of this new B&B variant, we conducted an experimental study on several NSP instances. The results show that our algorithm is able to return optimal schedules in acceptable running 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) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".