Routing science in home care: less travel without weaker continuity

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 Caire Core routing layer optimization engine—achieves the only feasible balance between continuity, legality, and efficiency.

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 Caire Core routing layer 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:

350! × C(377,27) ≈ 10 753

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).

• assign each visit to a caregiver
• order the visits within each caregiver's route

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.

• Swedish labor law (rest periods, breaks, weekly rest, maximum hours)
• Union and municipal requirements
• Time windows (earliest/latest, soft/hard)
• Travel times & geography
• Client–caregiver continuity
• Skills and certification requirements
• Reasonable workload & unused time
• Coordination of breaks and lunch periods

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:

• there is a subset of feasible schedules , and
• the solver selects one of the best (optimal or near-optimal) according to the objective function.

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 caregiver becomes sick
• a visit takes 7 minutes longer
• traffic increases
• a new client is added
• a client cancels
• continuity requires a specific match
• availability changes
• legal rules collide with real-time delays

A slinga is a static weekly pattern created by humans.

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.

• the slinga leaves the feasible region
• it becomes invalid
• replanning is required

the only workable architecture is:

• the gigantic search space (~10⁷⁵³)
• the microscopic feasible region
• the constantly moving constraints
• the fragility of slingor
• the need for real-time adaptation

→ encode tacit knowledge, continuity, geography, relationships → define baseline structure

• → encode tacit knowledge, continuity, geography, relationships
• → define baseline structure

This hybrid loop is not a convenience — it is a mathematical necessity .

• → evaluates millions of alternatives
• → tracks moving feasibility
• → maintains legal compliance
• → preserves stability
• → minimizes disruption
• → finds a new optimal schedule whenever reality changes

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.

Continuity layer: Each client-to-caregiver promise adds a bipartite constraint; breaking one ripples across the entire day. Breaks & fairness: Paid vs unpaid breaks plus fairness windows create temporal holes that humans fill by intuition but solvers evaluate in milliseconds. Disruptions: Every sick leave instance converts the deterministic problem into a stochastic VRPTW, proven PSPACE-hard. TSP VRPTW HHCRSP Multi-objective

• Continuity layer: Each client-to-caregiver promise adds a bipartite constraint; breaking one ripples across the entire day.
• Breaks & fairness: Paid vs unpaid breaks plus fairness windows create temporal holes that humans fill by intuition but solvers evaluate in milliseconds.
• Disruptions: Every sick leave instance converts the deterministic problem into a stochastic VRPTW, proven PSPACE-hard.

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.

Human planners: Understand building access, qualitative promises, and acceptable disruption patterns. Caire Core routing layer engine: Guarantees legal feasibility, fairness, and scenario replay within seconds. Hybrid result: Planners pin 70–80% of visits in slingor for stability; the Caire Core routing layer engine primarily optimizes the remaining 20–30% of flexible visits (new clients, disruptions, urgent add-ons) and can partially optimize fixed slingor with limited impact (5–12%). 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

• Human planners: Understand building access, qualitative promises, and acceptable disruption patterns.
• Caire Core routing layer engine: Guarantees legal feasibility, fairness, and scenario replay within seconds.
• Hybrid result: Planners pin 70–80% of visits in slingor for stability; the Caire Core routing layer engine primarily optimizes the remaining 20–30% of flexible visits (new clients, disruptions, urgent add-ons) and can partially optimize fixed slingor with limited impact (5–12%).

flowchart TD A[Human planners define slingor] -->|Pinned constraints| B[CAIRE knowledge graph] B --> C[Caire Core routing layer engine metaheuristics] C -->|Optimized deltas| D[Diff view & KPIs] D -->|Approve| E[Published schedule] E -->|Execution feedback| B D -->|Reject| F[Manual edit sandbox] sequenceDiagram participant Planner participant CAIRE participant Solver participant Field Planner->>CAIRE: Pin slingor & soft limits CAIRE->>Solver: Provide constraints + history Solver-->>CAIRE: Optimized proposal + score deltas CAIRE-->>Planner: Diff view + explainability Planner->>CAIRE: Approve hybrid plan CAIRE->>Field: Publish & monitor execution Rasmussen et al. 2022 Eveborn et al. 2006 Solomon 1987 Deb 2001 (MOO) Optimization Case Studies

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:

Home care is not "delivery routing with people." It is a multi-layered human-service optimization problem.

Human planners are exceptionally skilled at:

A human planner typically explores 10–15 local swaps mentally before overload. Solvers explore millions .

• Understanding client relationships
• Encoding tacit rules ("she prefers Anna on Tuesdays")
• Geographic intuition ("that elevator is always slow")
• Maintaining stable weekly patterns
• Evaluate millions of possible alternative schedules
• Globally minimize travel time
• Adapt instantly to disruptions
• Balance fairness scores mathematically

Solvers are exceptional at:

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

• Large-neighborhood search
• Constraint satisfaction
• Global optimization
• Mathematical fairness
• Real-time recomputation
• Understand patient relationships
• Interpret contextual history
• Reason about unstructured qualitative constraints

CAIRE's scheduling architecture combines human and machine strengths in three phases:

Humans define stable baselines Continuity and qualitative constraints embedded Solver verifies legality and feasibility

• Humans define stable baselines
• Continuity and qualitative constraints embedded
• Solver verifies legality and feasibility

Evaluates millions of alternatives Minimizes travel Balances workload Respects hard and soft time windows Adapts to new clients Handles lunchtime adherence and overtime limits

• Evaluates millions of alternatives
• Minimizes travel
• Balances workload
• Respects hard and soft time windows
• Adapts to new clients
• Handles lunchtime adherence and overtime limits

This hybrid loop yields: stable patterns, higher continuity, significantly reduced travel, higher service hours, reduced planner stress, and predictable operations.

• When disruptions occur (sickness, delays, cancellations, urgent add-ons)
• The solver recalculates all remaining visits in seconds
• Preserves the human-designed structure

Multiple peer-reviewed studies confirm the benefits of hybrid optimization:

10–20% increase in caregiver utilization (when AI optimizes flexible visits outside slingor) 5–12% increase in service hours / shift hours (when AI partially optimizes even fixed slingor) 15–25% reduction in travel time for flexible visits and during disruptions 20–40% fewer missed SLAs during real-time replanning Fewer overtime violations Lower planner workload Higher client continuity

• 10–20% increase in caregiver utilization (when AI optimizes flexible visits outside slingor)
• 5–12% increase in service hours / shift hours (when AI partially optimizes even fixed slingor)
• 15–25% reduction in travel time for flexible visits and during disruptions
• 20–40% fewer missed SLAs during real-time replanning
• Fewer overtime violations
• Lower planner workload
• Higher client continuity

Rasmussen et al. (2022). Home Care Scheduling Problem – A Review. Eveborn et al. (2006). Optimization of Home Care Planning and Scheduling. Solomon (1987). VRPTW Algorithms. Ernst et al. (2004). Scheduling and Rostering Review. Deb (2001). Multi-Objective Optimization.

• Rasmussen et al. (2022). Home Care Scheduling Problem – A Review.
• Eveborn et al. (2006). Optimization of Home Care Planning and Scheduling.
• Solomon (1987). VRPTW Algorithms.
• Ernst et al. (2004). Scheduling and Rostering Review.
• Deb (2001). Multi-Objective 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.

• 28 caregivers
• 350 visits per day (07–22, >10 visits per shift)
• 70–80% of visits are locked in slingor (stable weekly patterns)
• 20–30% flexible visits optimized with AI (new clients, disruptions, urgent add-ons)
• Higher service time per shift → more billable care time
• Reduced travel time for flexible visits → fewer overtime needs
• Faster replanning during disruptions → lower planner workload
• Better continuity → fewer complaints and higher quality

Modern Caire Core routing layer 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.

• 500,000+ visits per optimization run
• 100,000+ caregivers simultaneously
• Complex constraints and multi-day scheduling
• Real-time re-optimization in seconds, not minutes

When evaluating Field Service Routing (Caire Core routing layer) engines for home-care scheduling, there are several critical factors to consider:

Look for: Travel time reductions: 15–25% is typical for well-configured systems Balanced workload distribution: No caregiver should be systematically over- or under-loaded Highly consistent on-time arrival rates: Measurably better than manual planning Continuity preservation: Maintains client–caregiver relationships while minimizing travel

• Travel time reductions: 15–25% is typical for well-configured systems
• Balanced workload distribution: No caregiver should be systematically over- or under-loaded
• Highly consistent on-time arrival rates: Measurably better than manual planning
• Continuity preservation: Maintains client–caregiver relationships while minimizing travel

The engine should handle:

Modern Caire Core routing layer engines re-optimize in seconds, not minutes , which is critical for day-to-day operations.

• New visits dropped during the day
• Cancellations or overruns of visit durations
• Emergency visits requiring immediate replanning
• Caregiver absences or delays

Your Caire Core routing layer engine should comfortably handle:

• 100–10,000+ visits per run
• Dozens to thousands of caregivers simultaneously
• Complex constraints and multi-day scheduling
• Multi-objective optimization with multiple competing goals

Home care requires more than basic routing. Key capabilities include:

Consider both: Job-to-route computation time: Seconds for daily schedules, minutes for weekly schedules Consistency under load: Performance should not degrade significantly at high volumes Real-time re-optimization: Ability to recalculate in seconds when disruptions occur

• Job-to-route computation time: Seconds for daily schedules, minutes for weekly schedules
• Consistency under load: Performance should not degrade significantly at high volumes
• Real-time re-optimization: Ability to recalculate in seconds when disruptions occur

Routing APIs (like Google Maps routing) can compute a single route between two points, but they cannot:

Caire Core routing layer optimization engines are purpose-built to solve these multi-constraint, multi-objective problems and deliver complete optimized schedules, not just individual routes.

• Assign visits across many caregivers
• Respect complex skills or SLAs
• Rebalance workloads
• Produce multi-stop, multi-day plans
• Optimize across thousands of visits
• Re-optimize continuously during the day

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.

• Humans provide continuity, context, and qualitative insight.
• Solvers provide global optimization, fairness, and real-time computation.

The TSP seeks the shortest tour that visits every location once. Its search space grows as n!, making brute force impossible even for 50 stops. Every caregiver effectively solves a TSP-like sub-problem daily.

VRPTW extends TSP to multiple routes with earliest and latest service times. Swedish municipalities often require two overlapping windows per client, fracturing the feasible region into thousands of micro pockets.

HHCRSP combines routing, staff assignment, skills, continuity, and labor regulations. It is recognized as one of the hardest NP-hard problems because every constraint interacts with geography and human relationships.

Home care must maximize service-time %, minimize travel, protect continuity, limit overtime, and remain fair. These goals conflict, so CAIRE uses weighted score functions and metaheuristics instead of a single static formula.