Fertilizer Delivery Routing
VEHICLE ROUTING WITH TIME WINDOWS
Route optimization for custom fertilizer applicators can reduce fuel costs by 15–25% and ensure time-sensitive applications are completed within optimal agronomic windows. Each spring, a depot must decide which truck visits which fields and in what order, all within narrow crew-availability windows. This is the Vehicle Routing Problem with Time Windows (VRPTW) — NP-hard and one of the most studied problems in operations research.
Where This Decision Fits
Agricultural growing-season operations — the highlighted step is what this page optimizes
The Problem
From fertilizer depots to optimization theory
A fertilizer depot must deliver to 8 farm fields using 2 trucks with limited capacity. Each field has a time window — fertilizer must arrive during specific hours when crews are available. The goal is to minimize total travel distance while respecting capacity and time window constraints.
This is the Vehicle Routing Problem with Time Windows (VRPTW): extend CVRP with arrival time constraints [ei, li] at each customer.
| Agriculture Domain | VRPTW Model | |
|---|---|---|
| Fertilizer depot | Depot (node 0) | |
| Farm field | Customer node | |
| Delivery truck | Vehicle (capacity Q) | |
| Crew availability | Time window [ei, li] | |
| Fertilizer tons | Demand di |
Try It Yourself
Edit field locations, demands & time windows, then route your trucks optimally
Field Data & Truck Configuration
8 Fields · Click any cell to edit| Field | X | Y | Demand (t) | Window Start | Window End |
|---|
The Algorithms
Two construction heuristics — different strategies for building feasible routes
Nearest Neighbor with Time Windows
Start at Depot
Begin a new route from the depot with full truck capacity and time = 0.
Find Nearest Feasible
Among unvisited fields, find the nearest one whose time window and capacity constraints are satisfied.
Visit or Return
If a feasible field exists, visit it (updating time and remaining capacity). Otherwise, return to depot and start a new route.
Repeat
Continue until all fields are visited. Return final truck to depot.
Savings Heuristic (Clarke-Wright adapted for TW)
Initialize Individual Routes
Start with one route per field: Depot → Fieldi → Depot.
Compute Savings
For every pair (i, j), compute s(i,j) = d(Depot,i) + d(Depot,j) − d(i,j). A large saving means combining those fields into one route saves the most distance.
Merge by Savings
Sort savings descending. Merge route ending at i with route starting at j if capacity and time window constraints are satisfied.
Output Routes
The remaining (unmerged) routes are the final solution. Fewer routes = fewer trucks needed.
Real-World Complexity
Factors beyond the basic VRPTW model
Road Conditions
Unpaved farm roads may be impassable after rain, changing feasible routes.
Product Compatibility
Different fertilizer types cannot be mixed in the same truck compartment.
Weight Limits
Bridge and road weight restrictions limit truck loads on certain routes.
Seasonal Peaks
Spring application windows create extreme demand peaks with tight deadlines.
Wind Restrictions
Liquid fertilizer application is restricted during high winds, shrinking windows.
Loading Time
Truck loading at depot takes significant time, affecting departure schedules.
References
Key literature on vehicle routing with time windows