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

2026-07-06

AI Summary

This work addresses the NP-hard problem of shift scheduling that simultaneously satisfies complex hard constraints—such as labor regulations, mandatory rest periods, and cross-midnight shifts—and optimizes multiple soft objectives, including employee preferences and workload fairness. The authors propose a declarative, configurable framework based on CP-SAT, enabling flexible specification of 14 hard constraints and 15 soft objectives via JSON without code modification, thereby guaranteeing zero-constraint violations and enabling trade-offs among objectives. Key innovations include shift-window variable decomposition for centralized rest enforcement, a sensitivity-weighted workload fairness mechanism, multi-granularity temporal modeling, inter-week stability preservation, and a grid-offset preprocessing technique for cross-midnight shifts. Experiments on INRC-II and 36 synthetic configurations demonstrate the framework’s efficiency in handling scheduling granularities from 30 minutes to 2 hours while strictly adhering to all hard constraints.

Abstract

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.

Problem

• workforce scheduling
• combinatorial optimization
• labor regulations
• schedule stability
• cross-midnight shifts

Innovation

• CP-SAT
• workforce scheduling
• multi-granularity temporal resolution
• acuity-weighted equity
• cross-midnight shifts