[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81924-en":3,"doc-seo-81924-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},81924,8796095461564,"Liam","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","CP-WSP A Declarative CP-SAT Framework for Configurable Multi-Constraint Workforce Scheduling","Workforce scheduling is an NP-hard combinatorial optimization problem requiring simultaneous satisfaction of labor regulations, coverage needs, employee preferences, and operational objectives. CP-WSP introduces a declarative CP-SAT framework that enforces 14 hard constraints as mathematically inviolable requirements and optimizes 15 soft objectives via a unified weighted penalty function. Configuration is driven by JSON, avoiding code changes. It supports mandatory break scheduling with midpoint control, acuity-weighted workload equity, demand-driven multi-granularity timing, inter-week stability, and cross-midnight shifts. Evaluation shows zero hard-violation schedules by construction, proven optimality on INRC-II n005w4, and strong benchmark scaling.","CP-WSP: A Declarative CP-SAT Framework for Configurable Multi-Constraint Workforce Scheduling  \nVipul Patel 1 , Anirudh Deodhar 1 , Dagnachew Birru 1  \n1Phi Labs, Quantiphi  \n{vipul.patel, anirudh.deodhar, [dagnachew.birru](dagnachew.birru}@quantiphi.com)[}](dagnachew.birru}@quantiphi.com)[@quantiphi.com](dagnachew.birru}@quantiphi.com)  \narXiv :2607 .05 177v 1 [ cs .AI] 6 Jul 2026  \nAbstract  \nWorkforce 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; acuityweighted 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 (x = w − b) 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, CP-WSP achieves: zero hard-constraint violations across all instances by construction; proven optimality on INRC-II n005w4 (objective 118, gap 0.0%, 104 s); feasible solutions for 30-employee instances within 120 seconds; and model sizes scaling linearly at ∼4 ,400 variables per employee. The formulation enforces 29 total constraints (14 hard + 15 soft) -nearly three times the 6-12 constraint industry average. A constraint ablation study shows the full model achieves a 37% objective improvement over baseline, with workload equity delivering 66% fairness improvement at negligible coverage cost.  \n1 Introduction  \nWorkforce scheduling assigns employees to time slots to meet demand subject to hard labor constraints and soft quality objectives. It is NP-hard (Garey and Johnson 1979; Blazewicz, Lenstra, and Rinnooy Kan 1983) and arises in healthcare, retail and logistics. In practice, constraint sets are heterogeneous and evolving: labor laws mandate rest  \nAccepted at the CASP:ER Workshop, ICAPS 2026 . This is the authors’ version of the work.  \nand shift limits; operations require staffing floors and management coverage; employee contracts restrict availability; quality objectives include fairness and schedule stability. A schedule that violates a minimum rest requirement is not merely a “slightly suboptimal” solution-it is a regulatory violation with direct safety and legal implications, motivating the use of exact methods with formal feasibility guarantees.  \nExisting approaches-metaheuristics (Burke et al. 2006), integer programming (Vossen et al. 2015) and constraint programming (van Hoeve et al. 2006) -typically model 6-12 constraints at shift-level granularity (Table 1) . No reviewed system simultaneously supports mandatory break scheduling with midpoint control, acuity-weighted workload equity, inter-week schedule stability, cross-midnight shifts (e.g., 22:00-07:00) and configurable multi-granularity temporal resolution. Moreover, metaheuristic methods encode regulations as penalty terms rather than hard constraints, so generated schedules may violate rest or unavailability requirements. 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