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JAOT

Agricultural Planning

Optimize crop planning, fertilizer application, and harvest scheduling to maximize yield and minimize input costs. Agricultural operations involve balancing land, water, nutrients, and labor across multiple fields and seasons -- a natural fit for optimization.

When to Use This Guide

This guide is a good fit when you need to:

  • Crop rotation planning -- decide which crops to plant in each field across seasons to maintain soil health and maximize revenue
  • Fertilizer blending -- mix raw nutrients into a least-cost blend that meets crop-specific NPK requirements
  • Irrigation scheduling -- allocate limited water resources across fields based on crop needs and weather forecasts
  • Harvest logistics -- schedule harvesting crews and equipment across fields to minimize spoilage and transport costs

If your problem involves allocating land, water, or nutrients across crops and fields subject to agronomic rules, start here.

Step-by-Step Walkthrough

  1. Map your fields. Record each field's area, soil type, and current nutrient levels.

  2. List candidate crops. For each crop, note its water needs, nutrient requirements, expected yield, and market price.

  3. Define constraints. Typical constraints include total water supply, crop rotation rules (no wheat after wheat), minimum production targets for contracts, and labor availability.

  4. Choose your objective. Maximize total revenue from crop sales, minimize total fertilizer cost, or maximize yield subject to a budget cap.

  5. Run and interpret. The solver returns the optimal crop-to-field assignment for each season. Review for practical considerations like equipment compatibility.

Example: Seasonal Crop Rotation

Plan crop rotation for 6 fields over 3 seasons. Each field can grow one crop per season. Three crops are available (wheat, corn, soybeans) with different revenue, water needs, and rotation rules. Total water per season is limited.

import httpx

API_URL = "https://api.jaot.io/api/v2"
headers = {"Authorization": "Bearer ok_live_your_key_here"}

fields = [f"field_{i}" for i in range(1, 7)]
seasons = ["spring", "summer", "fall"]
crops = ["wheat", "corn", "soybeans"]

# Revenue per field per season for each crop
revenue = {"wheat": 800, "corn": 1200, "soybeans": 900}

# Water units needed per field per season
water_need = {"wheat": 3, "corn": 5, "soybeans": 2}
water_supply = 20  # Total water units per season

# Binary: plant crop c in field f during season s
variables = [
    {"name": f"{f}_{s}_{c}", "type": "binary"}
    for f in fields for s in seasons for c in crops
]

# Maximize total revenue
objective = {
    "sense": "maximize",
    "coefficients": {
        f"{f}_{s}_{c}": revenue[c]
        for f in fields for s in seasons for c in crops
    },
}

constraints = []

# Each field grows exactly one crop per season
for f in fields:
    for s in seasons:
        constraints.append({
            "name": f"one_crop_{f}_{s}",
            "coefficients": {f"{f}_{s}_{c}": 1 for c in crops},
            "sense": "==",
            "rhs": 1,
        })

# Water supply limit per season
for s in seasons:
    constraints.append({
        "name": f"water_{s}",
        "coefficients": {
            f"{f}_{s}_{c}": water_need[c]
            for f in fields for c in crops
        },
        "sense": "<=",
        "rhs": water_supply,
    })

# Rotation: no wheat after wheat in the same field
for f in fields:
    for i in range(len(seasons) - 1):
        s1, s2 = seasons[i], seasons[i + 1]
        constraints.append({
            "name": f"rotation_{f}_{s1}_{s2}",
            "coefficients": {
                f"{f}_{s1}_wheat": 1,
                f"{f}_{s2}_wheat": 1,
            },
            "sense": "<=",
            "rhs": 1,
        })

response = httpx.post(f"{API_URL}/solve", headers=headers, json={
    "variables": variables,
    "objective": objective,
    "constraints": constraints,
})
result = response.json()

print(f"Status: {result['status']}")
print(f"Total revenue: ${result['objective_value']:.2f}")
for f in fields:
    for s in seasons:
        for c in crops:
            if result['solution'][f"{f}_{s}_{c}"] > 0.5:
                print(f"  {f} / {s}: {c}")

The solver assigns high-revenue corn where water permits, fills the rest with soybeans or wheat, and avoids back-to-back wheat plantings in any field.

Next Steps