Crop Transport Routing
Capacitated Vehicle Routing
Transport costs represent 5–10% of total crop value for commodity grains, and efficient truck routing during peak harvest reduces fuel consumption by 15–25% (USDA, 2020). Every harvest season requires deciding how to route a fleet of capacity-limited trucks across dozens of fields to collect grain and return it to the elevator. This is the Capacitated Vehicle Routing Problem (CVRP)—one of the foundational NP-hard problems in combinatorial optimization.
Where This Decision Fits
Post-harvest operations chain — the highlighted step is what this page optimizes
The Problem
From farm fields to optimization theory
After harvest, 10 fields have crops ready for pickup. A fleet of 3 trucks, each with a 15-ton capacity, must collect all crops and deliver them to the grain elevator (depot). The objective is to minimize total travel distance while ensuring no truck exceeds its weight limit.
This is precisely the structure of a Capacitated Vehicle Routing Problem (CVRP). Each field is a customer with a demand equal to its harvest quantity, each truck is a vehicle with limited capacity, and the grain elevator is the depot. Each truck departs from the depot, visits a subset of fields, and returns — forming a route that respects the 15-ton limit.
| Agriculture Domain | CVRP Model | |
|---|---|---|
| Field | Customer | |
| Grain elevator | Depot | |
| Truck | Vehicle | |
| Harvest quantity | Demand di | |
| Truck limit | Capacity Q | |
| Pickup route | Vehicle route |
Try It Yourself
Route 3 trucks across 10 fields using classic CVRP heuristics
Configuration
10 Fields · 3 Trucks · 15t Capacity| Field | Harvest (tons) | X | Y |
|---|---|---|---|
| Grain Elevator (depot) | 0 | 300 | 300 |
| North Corn | 5 | 150 | 80 |
| East Wheat | 4 | 480 | 150 |
| South Soybean | 6 | 200 | 480 |
| West Canola | 3 | 50 | 300 |
| Ridge Barley | 5 | 420 | 80 |
| Valley Oats | 4 | 480 | 400 |
| Hilltop Corn | 7 | 100 | 150 |
| Creek Wheat | 3 | 350 | 450 |
| Far Soybean | 5 | 500 | 300 |
| Plain Barley | 4 | 250 | 180 |
The Algorithm
Clarke-Wright savings heuristic for vehicle routing
Clarke-Wright Savings
The Clarke-Wright algorithm (1964) is the most widely used constructive heuristic for the CVRP. It starts with each customer served by a dedicated vehicle (trivial solution) and iteratively merges routes to reduce total distance. The key insight: serving two customers on the same route saves the detour back to the depot between them.
Initialize Trivial Routes
Create one route per customer: depot → customeri → depot. This is the worst-case feasible solution with maximum travel distance.
Compute Savings
For every pair of customers (i, j), calculate the savings from merging their routes: s(i,j) = d(0,i) + d(0,j) − d(i,j). A large savings means customers i and j are far from the depot but close to each other — ideal for the same route.
Sort and Merge
Sort all savings in descending order. For each pair (i, j) with highest remaining savings, merge their routes if: (a) i and j are on different routes, (b) both are at the exterior of their routes (first or last customer), and (c) the merged route does not exceed vehicle capacity Q.
Return Solution
When no more feasible merges exist, the remaining routes form the CVRP solution. The number of vehicles used is determined automatically by the algorithm.
Real-World Complexity
Why agricultural logistics goes beyond the basic model
Road Conditions
Unpaved farm roads, seasonal mud, and weight-restricted bridges create asymmetric travel times and forbidden links between fields.
Harvest Timing
Crops must be collected within tight time windows after harvest to prevent spoilage, adding time window constraints to the routing model.
Weight Restrictions
Different crop types have varying densities. A truck full of wheat weighs differently than one full of barley, requiring product-specific capacity modeling.
Fuel Costs
Fuel consumption depends on load weight and terrain. Loaded trucks consume more fuel, making the objective load-dependent rather than purely distance-based.
Loading Equipment
Grain augers and loaders may not be available at every field simultaneously, introducing resource constraints and setup times at each stop.
Storage Deadlines
The grain elevator has limited unloading capacity and operating hours, requiring staggered arrival times and potentially multiple trips per day.
References
Key literature on vehicle routing and logistics optimization