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.
What Makes a Good Solution? A high-quality VRP solution balances multiple objectives:
Core Quality Metrics 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. { "totalJobs" : 50 , "assignedJobs" : 48 , "unassigned" : [ "job-23" , "job-47" ], "feasibilityRate" : 96 }
Acceptable with partial planning enabled. { "totalJobs" : 50 , "assignedJobs" : 42 , "unassigned" : [ ... ], "feasibilityRate" : 84 }
Indicates capacity or constraint issues. 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 fleet60-85% : Optimal range - good efficiency with buffer> 85% : High utilization - limited flexibility> 95% : Over-stretched - risk of delays
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 }
4. Travel Efficiency Multiple metrics evaluate routing efficiency:
Total Distance & Time { "totalTravelDistanceInMeters" : 245000 , "totalTravelTimeInSeconds" : 28800 , "averageSpeed" : 30.6 // km/h }
Distance per Job Efficiency = Total Distance / Number of Jobs
Lower values indicate better clustering and routing.
Circuity Factor Circuity = Actual Distance / Direct Distance
Values close to 1.0 indicate direct routes.
5. Time-Based Metrics { "onTimeDeliveries" : 47 , "lateDeliveries" : 3 , "onTimeRate" : 0.94 , "averageDelay" : 780 // seconds }
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
Advanced Quality Indicators 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 }
{ "preferredResourceMatches" : 35 , "totalPreferences" : 40 , "preferenceRate" : 0.875 , "tagMatchRate" : 0.95 }
{ "hardWindowViolations" : 0 , "softWindowViolations" : 5 , "averageArrivalDeviation" : -300 , // 5 min early on average "windowComplianceRate" : 0.95 }
Cost Effectiveness Fleet Utilization
Overtime Analysis
Resource Efficiency
{ "totalResources" : 10 , "activeResources" : 7 , "utilizationRate" : 0.7 , "costPerJob" : 45.20 , "costPerKm" : 2.10 }
{ "regularHours" : 280 , "overtimeHours" : 15 , "overtimeRate" : 0.051 , "overtimeCost" : 450 , "percentOfTotalCost" : 0.08 }
{ "revenuePerRoute" : 850 , "costPerRoute" : 320 , "profitMargin" : 0.624 , "jobsPerResourceHour" : 2.3 }
Comparing Solutions When evaluating alternative solutions:
Multi-Criteria Comparison 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.
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 );
Improvement Strategies For Low Feasibility
Enable Partial Planning
{ "options" : { "partialPlanning" : true }}
Relax Constraints
Convert hard constraints to soft where possible
Add Resources
Increase fleet size or extend shifts
Review Requirements
Check if all constraints are necessary
For Poor Efficiency Reduce Travel
Minimize Wait
Optimize Routes
{ "weights" : { "travelTimeWeight" : 5 , "regionMinimisationWeight" : 10 } }
{ "weights" : { "waitTimeWeight" : 20 }, "options" : { "snapUnit" : 900 // 15-min slots } }
{ "options" : { "distanceMatrix" : { "enabled" : true , "traffic" : true } } }
For Imbalanced Workload { "options" : { "fairWorkloadPerResource" : true , "workloadSensitivity" : 0.1 , // 10% tolerance "weights" : { "workloadSpreadWeight" : 100 } } }
Monitoring Quality Over Time Track metrics to identify trends:
Daily Metrics
Weekly Trends
Monthly KPIs
{ "date" : "2024-03-15" , "metrics" : { "feasibilityRate" : 0.96 , "occupancy" : 0.78 , "onTimeRate" : 0.94 , "costPerJob" : 42.50 } }
{ "week" : "2024-W11" , "trends" : { "feasibility" : "+2%" , "efficiency" : "-5%" , "cost" : "+3%" , "satisfaction" : "stable" } }
{ "month" : "2024-03" , "kpis" : { "avgFeasibility" : 0.95 , "avgOccupancy" : 0.76 , "fleetUtilization" : 0.82 , "customerSatisfaction" : 4.2 } }
Quality Benchmarks Industry standards for different sectors:
Sector Feasibility Occupancy On-Time Fairness Parcel Delivery 98%+ 75-85% 95%+ 0.80+ Field Service 95%+ 65-75% 90%+ 0.85+ Food Delivery 99%+ 70-80% 98%+ 0.75+ Medical Transport 100% 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.
Best Practices Quality Management Guidelines :
Define Success Metrics : Establish clear KPIs before optimizationRegular Monitoring : Track metrics daily/weeklyIterative Improvement : Make small, measured changesBalance Trade-offs : No solution is perfect in all dimensionsDocument Decisions : Record why certain trade-offs were madeBenchmark 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
