Ema WhitepaperAugust 19, 2026
C-KASE - A Staged Pattern-Based Architecture for Large-Scale Employee Scheduling
We introduce the Constraint-Kernel Adaptive Scheduling Engine (C-KASE)
An architecture that decouples constraint definition from execution through a staged pipeline.
Large-scale employee scheduling must assign hundreds of workers across shifts while meeting complex regulatory, contractual, and operational constraints. We introduce the Constraint-Kernel Adaptive Scheduling Engine (C-KASE), which separates constraint definition from execution through a staged pipeline. Rules are normalized into a canonical Constraint Kernel and routed by type and temporal scope: intra-shift rules are handled during pattern generation, while inter-day and global rules are solved as sparse constraints using CP-SAT. Compared with traditional slot-level approaches, this pattern-based formulation offers structural advantages in rule-heavy environments. C-KASE also introduces a piecewise-convex coverage objective that approximates quadratic penalties using linear constraints, automated infeasibility diagnostics through slack relaxation, and an optional natural-language explainability layer. Preliminary experiments with up to 321 employees and 41 active constraints reached provably optimal solutions within two minutes while achieving over 105% demand coverage.
C-KASE by the numbers
Optimal in 0.0 seconds
A production-scale schedule for 321 employees across 4 organizational units, solved to provably optimal status by the CP-SAT solver in under two minutes.
0.0% demand coverage
24,473 capacity units scheduled against 23,137 required — near-zero understaffing, with controlled overstaffing distributed by the piecewise-convex equalization penalty.
All 0 constraints verified
Legal, contractual, operational, and preference constraints active simultaneously — every one confirmed satisfied by an independent verifier, with the solver reaching optimal in about 60 seconds.
R² = 0.000 for headcount
Across 30 benchmark runs on 9 axes, employee count had a negligible impact on solve time — runtime scales with constraint complexity, not workforce size.
What you'll learn
Here's what to expect in the paper:
- How a staged, pattern-based architecture decouples constraint definition from enforcement
- Why pattern-based formulations beat slot-level models in rule-heavy scheduling regimes
- How piecewise-convex coverage equalization approximates quadratic penalties using only linear constraints
- Benchmark results: provably optimal schedules for 321 employees in under two minutes, with all 41 constraints independently verified
