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Solution Quality Metrics

Understanding solution quality goes beyond simple feasibility. This guide explains the key metrics for evaluating VRP solutions, how to interpret them, and strategies for improvement.

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What Makes a Good Solution?

A high-quality VRP solution balances multiple objectives:

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Core Quality Metrics

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1. Feasibility Rate

The percentage of jobs successfully assigned: 
Feasibility Rate = (Assigned Jobs / Total Jobs) × 100%
  • Perfect (100%)
  • Good (95%+)
  • Poor (<90%)
{
  "totalJobs": 50,
  "assignedJobs": 50,
  "unassigned": [],
  "feasibilityRate": 100
}
Ideal scenario - all jobs scheduled.

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2. Occupancy

How full the schedule is in terms of work time versus available time: 
Occupancy = (Total Work Time / Total Available Time) × 100%
Work Time includes:
  • Travel time
  • Service time
  • Wait time (if any)
Available Time:
  • Shift duration minus breaks
{
  "occupancy": 0.78,  // 78% utilized
  "totalWorkTimeInSeconds": 28080,
  "totalAvailableTimeInSeconds": 36000,
  "breakdown": {
    "travelTime": 14400,  // 40%
    "serviceTime": 12600,  // 35%
    "waitTime": 1080       // 3%
  }
}
Interpreting Occupancy:
  • < 60%: Underutilized - consider reducing fleet
  • 60-85%: Optimal range - good efficiency with buffer
  • > 85%: High utilization - limited flexibility
  • > 95%: Over-stretched - risk of delays

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3. Workload Fairness

Measures how evenly work is distributed across resources: 
Fairness = 1 - (Standard Deviation / Mean Work Time)

{
  "workloadFairness": 0.85,
  "resourceWorkloads": [
    {"resource": "driver-1", "workTime": 420, "deviation": 15},
    {"resource": "driver-2", "workTime": 390, "deviation": -15},
    {"resource": "driver-3", "workTime": 405, "deviation": 0}
  ],
  "averageWorkTime": 405,
  "standardDeviation": 15
}

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4. Travel Efficiency

Multiple metrics evaluate routing efficiency:

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Total Distance & Time

{
  "totalTravelDistanceInMeters": 245000,
  "totalTravelTimeInSeconds": 28800,
  "averageSpeed": 30.6  // km/h
}

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Distance per Job

Efficiency = Total Distance / Number of Jobs
Lower values indicate better clustering and routing.

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Circuity Factor

Circuity = Actual Distance / Direct Distance
Values close to 1.0 indicate direct routes.

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5. Time-Based Metrics

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On-Time Performance

{
  "onTimeDeliveries": 47,
  "lateDeliveries": 3,
  "onTimeRate": 0.94,
  "averageDelay": 780  // seconds
}

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Wait Time Analysis

{
  "totalWaitTimeInSeconds": 3600,
  "jobsWithWaitTime": 8,
  "averageWaitPerJob": 450,
  "waitTimePercentage": 0.05  // 5% of total time
}
High wait times indicate:
  • Poor time window alignment
  • Suboptimal route sequencing
  • Need for dynamic scheduling

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Advanced Quality Indicators

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Service Level Metrics

  • Priority Fulfillment
  • Customer Preferences
  • Time Window Compliance
{
  "priorityLevels": {
    "high": {"total": 10, "assigned": 10, "rate": 1.0},
    "medium": {"total": 25, "assigned": 23, "rate": 0.92},
    "low": {"total": 15, "assigned": 12, "rate": 0.8}
  },
  "weightedFulfillment": 0.93
}

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Cost Effectiveness

{
  "totalResources": 10,
  "activeResources": 7,
  "utilizationRate": 0.7,
  "costPerJob": 45.20,
  "costPerKm": 2.10
}

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Comparing Solutions

When evaluating alternative solutions:

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Multi-Criteria Comparison

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Pareto Optimization

Often no single “best” solution exists. Consider Pareto-optimal solutions:
A solution is Pareto-optimal if improving one metric necessarily worsens another. Keep multiple Pareto-optimal solutions for different scenarios.

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Weighted Scoring

Create a composite score based on business priorities: 
const weights = {
  feasibility: 0.3,
  efficiency: 0.25,
  cost: 0.25,
  service: 0.2
};

const compositeScore = 
  (feasibilityRate * weights.feasibility) +
  (efficiencyScore * weights.efficiency) +
  (costScore * weights.cost) +
  (serviceScore * weights.service);

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Improvement Strategies

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For Low Feasibility

1

Enable Partial Planning

{"options": {"partialPlanning": true}}
2

Relax Constraints

Convert hard constraints to soft where possible
3

Add Resources

Increase fleet size or extend shifts
4

Review Requirements

Check if all constraints are necessary

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For Poor Efficiency

  • Reduce Travel
  • Minimize Wait
  • Optimize Routes
{
  "weights": {
    "travelTimeWeight": 5,
    "regionMinimisationWeight": 10
  }
}

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For Imbalanced Workload

{
  "options": {
    "fairWorkloadPerResource": true,
    "workloadSensitivity": 0.1,  // 10% tolerance
    "weights": {
      "workloadSpreadWeight": 100
    }
  }
}

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Monitoring Quality Over Time

Track metrics to identify trends: 
{
  "date": "2024-03-15",
  "metrics": {
    "feasibilityRate": 0.96,
    "occupancy": 0.78,
    "onTimeRate": 0.94,
    "costPerJob": 42.50
  }
}

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Quality Benchmarks

Industry standards for different sectors:
SectorFeasibilityOccupancyOn-TimeFairness
Parcel Delivery98%+75-85%95%+0.80+
Field Service95%+65-75%90%+0.85+
Food Delivery99%+70-80%98%+0.75+
Medical Transport100%60-70%99%+0.90+
Benchmarks vary by region, business model, and service level agreements. Use these as starting points and adjust based on your specific requirements.

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Best Practices

Quality Management Guidelines:
  1. Define Success Metrics: Establish clear KPIs before optimization
  2. Regular Monitoring: Track metrics daily/weekly
  3. Iterative Improvement: Make small, measured changes
  4. Balance Trade-offs: No solution is perfect in all dimensions
  5. Document Decisions: Record why certain trade-offs were made
  6. Benchmark Regularly: Compare against historical performance

Scoring System

Understand score components

Performance Guide

Optimize solution speed

Cost Optimization

Minimize operational costs

Unassigned Reasons

Fix quality issues