Production Planning

Production planning optimization decides how much of each product to make given limited resources like machine hours, labor, and raw materials. Define your products, constraints, and profit margins -- the solver finds the mix that maximizes your bottom line.

Step-by-Step Walkthrough

1. Define your products

List each product you manufacture along with its unit profit (or contribution margin). For example, you might produce desks, chairs, and bookshelves with different profit margins.

2. Identify resource constraints

Determine the shared resources that limit production. Common constraints include:

• Machine hours per shift (e.g., CNC machine, assembly line)
• Labor hours available per week
• Raw material inventory (wood, steel, fabric)
• Storage or warehouse capacity

3. Set resource consumption rates

For each product, define how much of each resource it consumes per unit. A desk might require 4 hours of CNC time and 8 board-feet of lumber, while a chair needs 2 hours and 3 board-feet.

4. Configure the optimization

Set the objective to maximize total profit. Add constraints for each resource, ensuring total consumption does not exceed availability.

5. Run and interpret results

The solver returns the optimal quantity of each product. Check which resources are fully utilized (binding constraints) and where slack exists -- binding constraints indicate where adding capacity would improve results.

Example Parameters

import httpx

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

response = httpx.post(f"{API_URL}/solve", headers=headers, json={
    "variables": [
        {"name": "desks", "type": "integer", "lb": 0},
        {"name": "chairs", "type": "integer", "lb": 0},
        {"name": "bookshelves", "type": "integer", "lb": 0},
    ],
    "objective": {
        "sense": "maximize",
        "coefficients": {"desks": 120, "chairs": 55, "bookshelves": 85},
    },
    "constraints": [
        {
            "name": "cnc_machine_hours",
            "coefficients": {"desks": 4, "chairs": 2, "bookshelves": 3},
            "sense": "<=",
            "rhs": 160,
        },
        {
            "name": "assembly_labor_hours",
            "coefficients": {"desks": 3, "chairs": 1.5, "bookshelves": 2},
            "sense": "<=",
            "rhs": 120,
        },
        {
            "name": "lumber_board_feet",
            "coefficients": {"desks": 8, "chairs": 3, "bookshelves": 6},
            "sense": "<=",
            "rhs": 500,
        },
    ],
})
result = response.json()

print(f"Optimal profit: ${result['objective_value']:.2f}")
for var in result["variables"]:
    print(f"  Produce {var['value']:.0f} {var['name']}")

Templates

• Production Planning Optimizer -- pre-configured model for multi-product scheduling with resource constraints
• Custom Optimization -- build a model tailored to your specific production environment

Next Steps

• Cutting & Packing -- Minimize material waste in cutting and packing operations intermediate
• Supply Chain Planning -- Coordinate procurement, production, and distribution across your value chain advanced
• Food & Beverage Production -- Apply production planning principles to recipe formulation and batch scheduling intermediate