arXiv:2607.05177cs.AImath.OC2026-07被引 1

提出可配置的员工排班框架,精确满足14个硬约束,优化15个软目标。

CP-WSP: A Declarative CP-SAT Framework for Configurable Multi-Constraint Workforce Scheduling

  • 用声明式方法建模14个不可违反的硬约束,通过JSON配置无需改代码。
  • 支持30分钟至2小时多粒度时间调度,实现跨午夜班次与工作量公平分配。
  • 适合需要合规排班、高灵活性和可复现测试的医疗/24小时运营场景。

员工排班是需同时满足劳动法规、人员偏好、覆盖需求和运营目标的NP难组合优化问题。现有约束规划(CP)模型通常仅处理6-12个简化约束,且缺乏对强制性休息时段(中点控制)、按能力加权的工作量均衡、子班次级时间粒度(支持按需配员)、周间排班稳定性以及24小时运营常见的跨午夜班次模式的显式支持。本文提出CP-WSP:一种声明式CP-SAT框架,将14个硬约束作为数学上不可违反的要求强制执行(构造上零违规),并通过统一加权惩罚函数优化15个软目标。所有配置通过JSON文件完成,无需代码修改。关键贡献包括:支持中点控制的休息时段分解变量;按能力加权的工作量均衡机制;从30分钟到2小时的多粒度时间分辨率;周间排班稳定性设计;用于跨午夜班次的网格偏移预处理技术;以及一个包含36个可复现配置的基准测试套件。在INRC-II基准数据集上,于小时级与班次级粒度进行评估,并涵盖36个合成配置。

原文摘要 · Abstract (English)

Workforce scheduling is an NP-hard combinatorial optimization problem requiring simultaneous satisfaction of labor regulations, coverage requirements, employee preferences and operational objectives. Existing CP formulations typically model simplified instances with 6-12 constraints at shift-level granularity and critically lack explicit support for: mandatory break scheduling with midpoint placement control; acuity weighted workload equity; sub-shift temporal granularity enabling demand-driven staffing; inter-week schedule stability; and cross-midnight shift patterns common in 24-hour operations. This paper presents CP-WSP: a declarative CP-SAT framework enforcing 14 hard constraints as mathematically inviolable requirements (zero regulatory violations by construction) while optimizing 15 soft objectives through a unified weighted penalty function -- all configurable via a JSON specification with no code changes required. Key contributions include: a shift-window variable decomposition enabling mandatory break scheduling with centrality control; acuity-weighted workload equity; multi-granularity temporal resolution from 30 minutes to 2 hours; inter-week schedule stability; a grid-offset preprocessing technique for cross-midnight shifts; and a reproducible 36-configuration benchmark suite for community comparison. Evaluated on INRC-II benchmarks at both hourly and shift-level granularity and on 36 synthetic configurations.

排班优化约束规划多粒度调度24小时运营

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