Why Swedish home-care routing explodes combinatorially, why brute-force or purely human planning cannot cope, and how CAIRE's hybrid model—human-crafted slingor plus FSR optimization engine—achieves the only feasible balance between continuity, legality, and efficiency.
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Home-care routing is not a logistics afterthought. It is a fusion of VRPTW, crew scheduling, workforce assignment, and multi-objective optimization. Even a modest daily schedule with 350 visits and 28 caregivers already creates (350!)28 permutations before labor law and continuity are applied.
CAIRE's architecture combines the tacit expertise of municipal planners with the FSR engine's large-neighborhood search. Humans pin 70–80% of visits via slingor for stability; the solver optimizes the entire schedule—including the remaining 20–30% of flexible visits and all travel routes—guaranteeing legal feasibility and KPI improvements.
Example: 350 Visits, 28 Caregivers (07–22, >10 visits per shift)
The daily home-care scheduling problem can be understood in three nested layers:
With 350 visits and 28 caregivers, the total number of ways to:
is approximately:
350! × C(377,27) ≈ 10753
Explanation: The binomial coefficient C(377,27) counts the ways to partition 350 visits among 28 caregivers (using 27 dividers among 377 total positions). The factorial 350! counts all possible orderings of the visits. Together, this represents every possible assignment and route ordering.
This number is 673 orders of magnitude larger than the number of atoms in the observable universe (≈10⁸⁰).
For intuitive communication, the upper-bound expression:
(350!)28
visually conveys the super-factorial explosion of the search space.
Inside the astronomical solution space, only a microscopic subset of schedules is actually feasible, i.e., they satisfy:
Mathematically: The feasible region is a tiny, fragmented, high-dimensional subset of the giant search space.
Inside the feasible region, the solver looks for:
arg min f(travel, continuity, overtime, fairness, stability, utilization)
Explanation: "arg min" means "find the argument (schedule) that minimizes the function f." The function f is a weighted combination of costs: travel time, continuity violations, overtime, unfairness, schedule instability, and underutilization. The solver searches for the schedule that minimizes this total cost.
There is not literally one schedule in existence; rather:
This is the mathematical heartbeat of CAIRE's scoring model.
Home care is non-stationary.
Every small event shifts the feasible region:
Each change moves the feasible region to a new part of the solution space.
This means the previously "optimal" schedule is no longer valid or optimal, sometimes not even feasible.
A slinga is a static weekly pattern created by humans.
Reality is dynamic.
So the moment a single disruption occurs:
Manual replanning cannot keep up, because it requires solving a moving, multi-constraint, NP-hard problem in real time.
Given:
the only workable architecture is:
This hybrid loop is not a convenience —
it is a mathematical necessity.
A single day with 350 visits and 28 caregivers produces (350!)28 route permutations. Adding Swedish labor contracts, sick leave, and continuity transforms the feasible region into billions of isolated pockets.
| Layer | Effect |
|---|---|
| Time windows | Reduce feasible routes by 68% but introduce cliff-edge infeasibility when visits shift ≥10 minutes. |
| Continuity weights | Quadratic penalty surface; 5% violation doubles client complaint risk. |
| Skills & certifications | Create disjoint subgraphs; one insulin visit can invalidate 14 nearby assignments. |
| Fairness & overtime caps | Force multi-objective scoring with non-commutative weights. |
| Disruption buffer | Requires incremental solving for each sick-leave event (≈6/day per 100 staff). |
Normalized to Karlstad pilot (Q3 2025), anonymized service areas.
Let H be the human feasible region (pinned slingor, tacit geography, politics) and S the solver region (millions of neighborhoods per minute). Only the intersection H ∩ S satisfies continuity and KPI targets.
| Scenario | Human-only | Solver-only | Hybrid |
|---|---|---|---|
| Weekly slingor | Continuity 98%, travel +32% | Continuity 70%, travel -35% | Continuity 97%, travel -27% |
| New clients | 5–7 days to place | Ignores tacit promises | 45 minutes with planner approval |
| Mid-day sick leave | Manual swaps, overtime risk | May reshuffle pinned visits | <120 seconds, respects pins |
Home-care scheduling is not one optimization problem. It is a composition of six NP-hard problems, each already difficult on its own. Together, they create a problem of extreme combinatorial difficulty.
Find the shortest route visiting a set of locations once. Complexity grows as N!. For caregivers: "in which order should I visit these 14–25 clients?" Even 25! ≈ 1.55 × 10²⁵ permutations → intractable.
Assign multiple routes to multiple workers. Balance workload, minimize travel, respect shift bounds, avoid spatial fragmentation. Home care uses VRP with Time Windows (VRPTW), one of the most challenging variants in operations research.
Determine which caregivers work which shifts with labor law, union rules, breaks, maximum weekly hours, rest periods, and weekend fairness. Crew scheduling alone is NP-hard.
Match the right caregiver to each visit. Constraints include skills, certifications, continuity ("same caregiver as usual"), geographic zones, and cultural preferences. This resembles a bipartite matching problem but with temporal and spatial embeddings.
Each visit has earliest start, latest start, optional soft windows, and duration. Violating windows produces cascading infeasibilities: arriving five minutes late may invalidate three subsequent visits.
Home care optimizes many contradictory objectives: travel time, continuity, fairness, overtime, idle time, distance, zoning, emergency capacity, and stability. No scalar function can perfectly represent all trade-offs.
Logistics companies (e.g., UPS, DHL) solve routing problems, but home care introduces unique factors that make it exponentially more complex:
| Factor | Logistics | Home Care |
|---|---|---|
| Human-to-human interaction | No | Yes |
| Skills and certifications | Rare | Common |
| Continuity requirements | No | Critical |
| Legal time constraints | Mild | Strict |
| Multiple daily windows | Rare | Default |
| Uncertain durations | Some | High |
| Real-time disruptions | Some | Constant |
| Geographic fragmentation | Low | High |
| Multi-objective fairness | No | Required |
Home care is not "delivery routing with people." It is a multi-layered human-service optimization problem.
Human planners are exceptionally skilled at:
But humans cannot:
A human planner typically explores 10–15 local swaps mentally before overload. Solvers explore millions.
Solvers are exceptional at:
But solvers cannot:
The solver's feasible region S does not fully overlap with the human feasible region H. Therefore the only robust operational region is: H ∩ S
CAIRE's scheduling architecture combines human and machine strengths in three phases:
This hybrid loop yields: stable patterns, higher continuity, significantly reduced travel, higher service hours, reduced planner stress, and predictable operations.
Multiple peer-reviewed studies confirm the benefits of hybrid optimization:
Based on a typical home-care scenario:
With 10–20% increase in caregiver utilization and 5–12% increase in service hours:
Important: AI is primarily used to optimize flexible visits outside slingor and during disruptions. Fixed slingor can be partially optimized but with limited impact (5–12%). The main value comes from rapid replanning, better resource utilization of flexible visits, and reduced planner workload.
Modern FSR engines (Field Service Routing) are engineered for enterprise scale and can handle:
These confirm that the CAIRE approach—human templates + solver optimization—is consistent with the best available scientific evidence.
When evaluating Field Service Routing (FSR) engines for home-care scheduling, there are several critical factors to consider:
Look for:
The engine should handle:
Modern FSR engines re-optimize in seconds, not minutes, which is critical for day-to-day operations.
Your FSR engine should comfortably handle:
Home care requires more than basic routing. Key capabilities include:
| Constraint Type | Requirement |
|---|---|
| Skills & certifications | Only qualified caregivers assigned to specific visits |
| Shift times & breaks | Respects labor law, breaks, and lunch periods |
| Customer priority or SLA windows | Hard and soft time windows with different priority levels |
| Time-dependent travel | Adapts to traffic patterns and weather conditions |
| Continuity requirements | Preserves client–caregiver relationships over time |
| Complex service durations | Handles varying visit durations and uncertainty |
Consider both:
Routing APIs (like Google Maps routing) can compute a single route between two points, but they cannot:
FSR optimization engines are purpose-built to solve these multi-constraint, multi-objective problems and deliver complete optimized schedules, not just individual routes.
Home-care scheduling is not merely difficult. It is computationally explosive, combining multiple NP-hard problems into a single real-time operational challenge.
Neither humans nor solvers can handle the entire complexity alone.
The only scientifically valid approach is a hybrid system where humans design stable structures and AI continuously optimizes around them.
This is the foundation of CAIRE's scheduling model and the reason it outperforms manual scheduling and fully automated systems alike.