AI 中文总结
针对居家护理资源分配，提出字典序目标LEX-COS，优先最小化连续性违规与加班，实验表明在多数实例中优于加权策略，且不增加任一指标。
AI 中文摘要
居家护理分配必须平衡护理连续性、护理人员加班以及护理人员与服务之间的兼容性。已发表的居家护理最优资源分配问题（HCORAP）的公式化表述使用加权策略（Weighted）来组合这些结果，允许兼容性的提升以牺牲较差的连续性或额外的加班为代价。我们引入了LEX-COS，一种针对HCORAP的字典序目标，它首先最小化连续性违规，然后最小化加班，最后最大化兼容性。我们给出了一个精确的MaxSAT实现，并构建了HCORAP-LC，一个可复现的、包含48个实例、具有有限护理人员容量的合成评估套件。与Weighted相比，LEX-COS在48个实例中的42个中减少了连续性违规和加班，在任何实例中都没有增加这两项指标，同时产生了较低的兼容性。在36个实例中，LEX-COS实现了比所有Weighted最优分配更好的连续性和更低的加班。在单独的48实例Original基准上，Gurobi和CPLEX这两个领先的商业MIP求解器，在两种策略下都能解决每个实例，并且比EvalMaxSAT快得多。EvalMaxSAT也在LEX-COS下解决了整个基准。在EvalMaxSAT内部，用Totalizer替换排序网络在Weighted下改善了运行时间，在LEX-COS下没有明显收益。这些结果刻画了在居家护理分配中给予连续性和加班明确优先级的效果。
英文摘要
Home-care allocation must balance continuity of care, caregiver overtime, and caregiver-service compatibility. The published formulation of the Home-Care Optimal Resource Allocation Problem (HCORAP) uses a weighted policy (Weighted) to combine these outcomes, allowing compatibility gains to offset poorer continuity or additional overtime. We introduce LEX-COS, a lexicographic objective for HCORAP that first minimizes continuity violations, then overtime, and finally maximizes compatibility. We give an exact MaxSAT implementation and construct HCORAP-LC, a reproducible 48-instance synthetic evaluation suite with limited caregiver capacity. Compared with Weighted, LEX-COS reduces both continuity violations and overtime in 42 of 48 instances, without increasing either measure in any instance, while yielding lower compatibility. In 36 instances, LEX-COS achieves better continuity and lower overtime than every Weighted-optimal allocation. On the separate 48-instance Original benchmark, Gurobi and CPLEX, two leading commercial MIP solvers, resolve every instance under both policies and are substantially faster than EvalMaxSAT. EvalMaxSAT also resolves the full benchmark under LEX-COS. Within EvalMaxSAT, replacing sorting networks with Totalizer improves runtime under Weighted, with no clear gain under LEX-COS. These results characterize the effects of giving continuity and overtime explicit priority in home-care allocation.
Comments5 pages, 2 figures, 2 tables. Submitted to ICIIT 2027
