从元启发式算法到精确方法：面向多目标医护人员排班的CP-SAT方法
From Metaheuristics to Exact Methods: A CP-SAT Approach for Multi-Objective Healthcare Workforce Scheduling
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- Phi Labs, Quantiphi（Quantiphi公司旗下Phi Labs）
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中文总结 AI 辅助
该研究针对医护排班问题，提出CP-SAT约束规划模型，可满足14个硬约束与15个软目标，在18个实例上验证了其零违规、最优性及可扩展性，服务质量较MOGA提升50-67%。
中文摘要 AI 辅助
医护人员排班是一个NP难优化问题，需同时满足劳动法规、覆盖要求、员工偏好和成本目标。现有方法（遗传算法、整数规划、约束规划）以班次级粒度建模6-12个约束，无法保证法规合规性，且缺乏对多角色多技能异质性、带中点控制的强制休息安排、 acuity加权工作量公平性、亚班次粒度、周间稳定性及跨午夜班次的支持。本文提出CP-SAT：一种面向多角色多技能医护排班的约束规划模型。CP-SAT强制14个硬约束以保证零法规违规，同时通过统一加权惩罚函数优化15个软目标。其贡献包括：支持带中心性控制的休息安排的班次窗口分解、acuity加权工作量公平性、15分钟至1天的多粒度分辨率、周间稳定性，以及网格偏移预处理将跨午夜班次映射为单个调度日而无需更改求解器。CP-SAT在18个实例上进行评估：5个合成医院单元（10-33名护士）、10个INRC-II基准（5-80名护士，最长8周调度周期）和3个兼容NRP-23的实例（10-25名护士，含跨午夜夜班）。结果：所有18个实例因构造原因无硬约束违规；INRC-II n005w4实例达到最优性（目标值118，差距0.0%，耗时104秒）；可扩展至含179800个变量和351425个约束的可行调度（80名护士）；服务质量较MOGA提升50-67%；模型规模以约每名员工4400个变量的近线性方式扩展。该模型共强制29个约束（14个硬约束、15个软约束），约为行业平均的三倍。
英文摘要
Healthcare workforce scheduling is an NP-hard optimization problem requiring simultaneous satisfaction of labor regulations, coverage requirements, employee preferences and cost objectives. Existing approaches (genetic algorithms, integer programming, constraint programming) model 6-12 constraints at shift-level granularity and cannot guarantee regulatory compliance. They also lack support for multi-role, multi-skill heterogeneity, mandatory break scheduling with midpoint control, acuity-weighted workload equity, sub-shift granularity, inter-week stability, and cross-midnight shifts. This paper presents CP-SAT: a Constraint Programming formulation for multi-role, multi-skill healthcare scheduling. CP-SAT enforces 14 hard constraints guaranteeing zero regulatory violations, while optimizing 15 soft objectives via a unified weighted penalty function. Contributions include a shift-window decomposition enabling break scheduling with centrality control, acuity-weighted workload equity, multi-granularity resolution from 15 minutes to 1 day, inter-week stability, and grid-offset preprocessing mapping cross-midnight shifts into a single scheduling day without solver changes. CP-SAT is evaluated on 18 instances: five synthetic hospital units (10-33 nurses), 10 INRC-II benchmarks (5-80 nurses, up to 8-week horizons) and 3 NRP-23 compatible instances (10-25 nurses) with cross-midnight Night shifts. Results: zero hard-constraint violations across all 18 instances by construction; proven optimality on INRC-II n005w4 (objective 118, gap 0.0%, 104s); feasible schedules scaling to 179,800 variables and 351,425 constraints (80 nurses); service quality improved 50-67% over MOGA; and model size scaling near-linearly at approximately 4,400 variables per employee. The formulation enforces 29 total constraints (14 hard, 15 soft), nearly three times the industry average.
