Production Planning

Version:

Experience level: Beginner
Reasoning types: Prescriptive
Industry: Manufacturing
Tags: AllocationMILP
Experience level: Beginner
Reasoning types: Prescriptive
Industry: Manufacturing
Tags: AllocationMILP
Experience level: Intermediate
Reasoning types: Prescriptive
Industry: Manufacturing
Tags: ProductionManufacturingScenario Analysis

What this template is for

Manufacturing teams often need to decide how much of each product to produce on each machine, given limited machine time and product demand targets. This template models a small production planning problem where:

Each product has a demand requirement and a per-unit profit.
Each machine has a limited number of available production hours.
Each machine–product route has a specific processing time (hours per unit).

The key challenge is that capacity is shared across products, so meeting demand for one product can crowd out more profitable production elsewhere. This template uses RelationalAI’s prescriptive reasoning (optimization) capabilities to compute a profit-maximizing production plan that meets demand while respecting machine capacity.

Who this is for

You want an end-to-end example of prescriptive reasoning (optimization) with RelationalAI.
You’re comfortable with basic Python and the idea of decision variables, constraints, and objectives.

What you’ll build

A semantic model of machines, products, and machine–product production rates using concepts and properties.
A MILP with one integer decision variable per feasible machine–product pair.
Constraints that enforce machine-hour capacity and product demand satisfaction.
A small scenario analysis loop that reruns the solve under different demand scaling assumptions.

What’s included

Model + solve script: production_planning.py
Sample data: data/products.csv, data/machines.csv, data/production_rates.csv
Outputs: solver status/objective per scenario, a per-scenario production plan table, and a scenario summary

Prerequisites

Access

A Snowflake account that has the RAI Native App installed.
A Snowflake user with permissions to access the RAI Native App.

Tools

Python >= 3.10

Quickstart

Follow these steps to run the template with the included sample data.

Download the ZIP file for this template and extract it:
Terminal window
```
curl -O https://private.relational.ai/templates/zips/v0.13/production_planning.zip
unzip production_planning.zip
cd production_planning
```
You can also download the template ZIP using the “Download ZIP” button at the top of this page.

Create and activate a virtual environment

python -m venv .venv
source .venv/bin/activate
python -m pip install -U pip

Install dependencies

From this folder:
Terminal window
```
python -m pip install .
```
Configure Snowflake connection and RAI profile
Terminal window
```
rai init
```
Run the template
Terminal window
```
python production_planning.py
```

Expected output

The script solves three demand scenarios and prints a production plan table for each. You should see output shaped like:

Running scenario: demand_multiplier = 1.0
  Status: OPTIMAL, Objective: 14945.0

  Production plan:
                  name  value
qty_Machine_1_Widget_A    4.0
qty_Machine_1_Widget_C   95.0
...

==================================================
Scenario Analysis Summary
==================================================
  0.8: OPTIMAL, obj=15020.0
  1.0: OPTIMAL, obj=14945.0
  1.1: OPTIMAL, obj=14770.0

Template structure

.
├─ README.md
├─ pyproject.toml
├─ production_planning.py      # main runner / entrypoint
└─ data/                       # sample input data
   ├─ products.csv
   ├─ machines.csv
   └─ production_rates.csv

Start here: production_planning.py

Sample data

Data files are in data/.

`products.csv`

Column	Meaning
`id`	Unique product identifier
`name`	Product name
`demand`	Units that must be produced (before scenario scaling)
`profit`	Profit per unit

`machines.csv`

Column	Meaning
`id`	Unique machine identifier
`name`	Machine name
`hours_available`	Total hours available (capacity)

`production_rates.csv`

Column	Meaning
`machine_id`	Foreign key to `machines.csv.id`
`product_id`	Foreign key to `products.csv.id`
`hours_per_unit`	Hours required to produce one unit on that machine

Model overview

The optimization model is built around four concepts.

`Product`

A product with demand and profit parameters.

Property	Type	Identifying?	Notes
`id`	int	Yes	Primary key loaded from `data/products.csv`
`name`	string	No	Used for variable naming in the output
`demand`	int	No	Minimum units required (scaled by `demand_multiplier`)
`profit`	float	No	Profit per unit in the objective

`Machine`

A production resource with limited available hours.

Property	Type	Identifying?	Notes
`id`	int	Yes	Primary key loaded from `data/machines.csv`
`name`	string	No	Used for variable naming in the output
`hours_available`	float	No	Capacity constraint per machine

`ProductionRate`

A feasible machine–product route that specifies how long it takes to produce one unit.

Property	Type	Identifying?	Notes
`machine`	`Machine`	Part of compound key	Joined via `data/production_rates.csv.machine_id`
`product`	`Product`	Part of compound key	Joined via `data/production_rates.csv.product_id`
`hours_per_unit`	float	No	Coefficient in the machine-capacity constraints

`Production` (decision concept)

One decision row per ProductionRate route; the solver chooses the production quantity.

Property	Type	Identifying?	Notes
`rate`	`ProductionRate`	Yes	One decision variable per machine–product route
`quantity`	float	No	Integer decision variable (`type="int"`), lower bounded by 0

How it works

This section walks through the highlights in production_planning.py.

Import libraries and configure inputs

First, the script imports the Semantics APIs and configures DATA_DIR and the pandas string inference behavior:

from pathlib import Path

import pandas
from pandas import read_csv

from relationalai.semantics import Model, data, define, require, sum, where
from relationalai.semantics.reasoners.optimization import Solver, SolverModel

# --------------------------------------------------
# Configure inputs
# --------------------------------------------------

DATA_DIR = Path(__file__).parent / "data"

# Disable pandas inference of string types. This ensures that string columns
# in the CSVs are loaded as object dtype. This is only required when using
# relationalai versions prior to v1.0.
pandas.options.future.infer_string = False

# --------------------------------------------------
# Define semantic model & load data
# --------------------------------------------------

# Create a Semantics model container.
model = Model("production_planning", config=globals().get("config", None), use_lqp=False)

Define concepts and load CSV data

Next, the script defines Product and Machine, loads products.csv and machines.csv via data(...).into(...), and then joins the foreign keys in production_rates.csv to create ProductionRate rows using where(...).define(...):

# Product concept: products with demand and profit per unit.
Product = model.Concept("Product")
Product.id = model.Property("{Product} has {id:int}")
Product.name = model.Property("{Product} has {name:string}")
Product.demand = model.Property("{Product} has {demand:int}")
Product.profit = model.Property("{Product} has {profit:float}")

# Load product data from CSV.
data(read_csv(DATA_DIR / "products.csv")).into(Product, keys=["id"])

# Machine concept: machines with a limited number of available production hours.
Machine = model.Concept("Machine")
Machine.id = model.Property("{Machine} has {id:int}")
Machine.name = model.Property("{Machine} has {name:string}")
Machine.hours_available = model.Property("{Machine} has {hours_available:float}")

# Load machine data from CSV.
data(read_csv(DATA_DIR / "machines.csv")).into(Machine, keys=["id"])

# ProductionRate concept: hours required per unit for each machine-product pair.
Rate = model.Concept("ProductionRate")
Rate.machine = model.Property("{ProductionRate} on {machine:Machine}")
Rate.product = model.Property("{ProductionRate} for {product:Product}")
Rate.hours_per_unit = model.Property("{ProductionRate} has {hours_per_unit:float}")

# Load production rate data from CSV.
rates_data = data(read_csv(DATA_DIR / "production_rates.csv"))

# Define ProductionRate entities by joining the rate CSV with Machine and Product.
where(
    Machine.id == rates_data.machine_id,
    Product.id == rates_data.product_id
).define(
    Rate.new(machine=Machine, product=Product, hours_per_unit=rates_data.hours_per_unit)
)

Define decision variables, constraints, and objective

Then the script creates a Production decision concept (one row per ProductionRate) and defines a build_formulation helper. That helper registers the integer decision variable with solve_for(...), adds constraints with require(...), and sets a profit-maximizing objective:

# Production decision concept: production quantity for each machine-product pair.
Production = model.Concept("Production")
Production.rate = model.Property("{Production} uses {rate:ProductionRate}")
Production.x_quantity = model.Property("{Production} has {quantity:float}")
define(Production.new(rate=Rate))

Prod = Production.ref()

# Scenario parameter (overridden within the scenario loop).
demand_multiplier = 1.0


def build_formulation(s):
    """Register variables, constraints, and objective on the solver model."""
    # Variable: production quantity (integer)
    s.solve_for(
        Production.x_quantity,
        name=[
            "qty",
            Production.rate.machine.name,
            Production.rate.product.name,
        ],
        lower=0,
        type="int",
    )

    # Constraint: machine capacity
    machine_hours = (
        sum(Prod.quantity * Prod.rate.hours_per_unit)
        .where(Prod.rate.machine == Machine)
        .per(Machine)
    )
    capacity_limit = require(machine_hours <= Machine.hours_available)
    s.satisfy(capacity_limit)

    # Constraint: meet demand (scaled by demand_multiplier)
    product_qty = sum(Prod.quantity).where(Prod.rate.product == Product).per(Product)
    meet_demand = require(product_qty >= Product.demand * demand_multiplier)
    s.satisfy(meet_demand)

    # Objective: maximize total profit
    total_profit = sum(Production.x_quantity * Production.rate.product.profit)
    s.maximize(total_profit)

Solve scenarios and print results

Finally, the script runs a small scenario analysis by setting demand_multiplier, solving a fresh SolverModel each time, and printing a filtered production plan table (only rows where the solver value is greater than 0.001):

SCENARIO_PARAM = "demand_multiplier"
SCENARIO_VALUES = [0.8, 1.0, 1.1]

scenario_results = []

for scenario_value in SCENARIO_VALUES:
    print(f"\nRunning scenario: {SCENARIO_PARAM} = {scenario_value}")

    # Set scenario parameter value
    demand_multiplier = scenario_value

    # Create fresh SolverModel for each scenario.
    s = SolverModel(model, "cont")
    build_formulation(s)

    solver = Solver("highs")
    s.solve(solver, time_limit_sec=60)

    scenario_results.append(
        {
            "scenario": scenario_value,
            "status": str(s.termination_status),
            "objective": s.objective_value,
        }
    )
    print(f"  Status: {s.termination_status}, Objective: {s.objective_value}")

    # Print production plan from solver results
    var_df = s.variable_values().to_df()
    qty_df = var_df[
        var_df["name"].str.startswith("qty") & (var_df["float"] > 0.001)
    ].rename(columns={"float": "value"})
    print(f"\n  Production plan:")
    print(qty_df.to_string(index=False))

# Summary
print("\n" + "=" * 50)
print("Scenario Analysis Summary")
print("=" * 50)
for result in scenario_results:
    print(f"  {result['scenario']}: {result['status']}, obj={result['objective']}")

Customize this template

Change the scenario parameters

This template includes a simple demand sensitivity analysis controlled by demand_multiplier.

Parameter	Type	Values	Description
`demand_multiplier`	numeric	`0.8`, `1.0`, `1.1`	Multiplier applied to all product demands

How to customize the scenarios:

In production_planning.py, edit SCENARIO_VALUES to the multipliers you want to test.

How to interpret results:

If increasing demand_multiplier decreases the objective, demand is forcing production into less-profitable routes.
If changing demand_multiplier does not change the objective, the demand constraints are likely non-binding at those values.

Use your own data

Replace the CSV files under data/.
Keep IDs consistent across files (machine_id / product_id must exist in machines.csv / products.csv).

Extend the model

Add setup costs and binary on/off decisions per route.
Add maximum production limits per product (demand as an upper bound rather than a lower bound).
Add multi-period planning (introduce a Period concept and inventory/transition constraints).

Troubleshooting

Why does authentication/configuration fail?

Run rai init to create/update raiconfig.toml.
If you have multiple profiles, set RAI_PROFILE or switch profiles in your config.

Why does the script fail to connect to the RAI Native App?

Verify the Snowflake account/role/warehouse and rai_app_name are correct in raiconfig.toml.
Ensure the RAI Native App is installed and you have access.

ModuleNotFoundError when running the script

Confirm your virtual environment is activated.
Install the template dependencies from this folder: python -m pip install .

CSV loading fails (missing file or column)

Confirm the CSVs exist under data/ and the filenames match.
Ensure the headers match the expected schema:
- products.csv: id, name, demand, profit
- machines.csv: id, name, hours_available
- production_rates.csv: machine_id, product_id, hours_per_unit

Why do I get Status: INFEASIBLE?

Check that total machine hours are sufficient to meet demand: for each product, at least one route must exist in production_rates.csv.
If you increased demand_multiplier, try lowering it or increasing hours_available.

Why is the production plan empty?

The output filters on float > 0.001 and only prints variables whose names start with qty.
If you suspect near-zero values, print s.variable_values().to_df() without filtering.

Solver fails or returns an unexpected termination status

Try re-running; transient connectivity issues can affect the solve step.
If the solve is slow, reduce problem size (fewer machines/products/routes) or increase time_limit_sec in production_planning.py.

What this template is for

Each product has a demand requirement and a per-unit profit.
Each machine has a limited number of available production hours.
Each machine–product route has a specific processing time (hours per unit).

Who this is for

You want an end-to-end example of prescriptive reasoning (optimization) with RelationalAI.
You’re comfortable with basic Python and the idea of decision variables, constraints, and objectives.

What you’ll build

A semantic model of machines, products, and machine–product production rates using concepts and properties.
A MILP with one integer decision variable per feasible machine–product pair.
Constraints that enforce machine-hour capacity and product demand satisfaction.
A small scenario analysis loop that reruns the solve under different demand scaling assumptions.

What’s included

Model + solve script: production_planning.py
Sample data: data/products.csv, data/machines.csv, data/production_rates.csv
Outputs: solver status/objective per scenario, a per-scenario production plan table, and a scenario summary

Prerequisites

Access

A Snowflake account that has the RAI Native App installed.
A Snowflake user with permissions to access the RAI Native App.

Tools

Python >= 3.10

Quickstart

Follow these steps to run the template with the included sample data.

Download the ZIP file for this template and extract it:
Terminal window
```
curl -O https://private.relational.ai/templates/zips/v0.14/production_planning.zip
unzip production_planning.zip
cd production_planning
```
You can also download the template ZIP using the “Download ZIP” button at the top of this page.

Create and activate a virtual environment

python -m venv .venv
source .venv/bin/activate
python -m pip install -U pip

Install dependencies

From this folder:
Terminal window
```
python -m pip install .
```
Configure Snowflake connection and RAI profile
Terminal window
```
rai init
```
Run the template
Terminal window
```
python production_planning.py
```

Expected output

The script solves three demand scenarios and prints a production plan table for each. You should see output shaped like:

Running scenario: demand_multiplier = 1.0
  Status: OPTIMAL, Objective: 14945.0

  Production plan:
                  name  value
qty_Machine_1_Widget_A    4.0
qty_Machine_1_Widget_C   95.0
...

==================================================
Scenario Analysis Summary
==================================================
  0.8: OPTIMAL, obj=15020.0
  1.0: OPTIMAL, obj=14945.0
  1.1: OPTIMAL, obj=14770.0

Template structure

.
├─ README.md
├─ pyproject.toml
├─ production_planning.py      # main runner / entrypoint
└─ data/                       # sample input data
   ├─ products.csv
   ├─ machines.csv
   └─ production_rates.csv

Start here: production_planning.py

Sample data

Data files are in data/.

`products.csv`

Column	Meaning
`id`	Unique product identifier
`name`	Product name
`demand`	Units that must be produced (before scenario scaling)
`profit`	Profit per unit

`machines.csv`

Column	Meaning
`id`	Unique machine identifier
`name`	Machine name
`hours_available`	Total hours available (capacity)

`production_rates.csv`

Column	Meaning
`machine_id`	Foreign key to `machines.csv.id`
`product_id`	Foreign key to `products.csv.id`
`hours_per_unit`	Hours required to produce one unit on that machine

Model overview

The optimization model is built around four concepts.

`Product`

A product with demand and profit parameters.

Property	Type	Identifying?	Notes
`id`	int	Yes	Primary key loaded from `data/products.csv`
`name`	string	No	Used for variable naming in the output
`demand`	int	No	Minimum units required (scaled by `demand_multiplier`)
`profit`	float	No	Profit per unit in the objective

`Machine`

A production resource with limited available hours.

Property	Type	Identifying?	Notes
`id`	int	Yes	Primary key loaded from `data/machines.csv`
`name`	string	No	Used for variable naming in the output
`hours_available`	float	No	Capacity constraint per machine

`ProductionRate`

A feasible machine–product route that specifies how long it takes to produce one unit.

Property	Type	Identifying?	Notes
`machine`	`Machine`	Part of compound key	Joined via `data/production_rates.csv.machine_id`
`product`	`Product`	Part of compound key	Joined via `data/production_rates.csv.product_id`
`hours_per_unit`	float	No	Coefficient in the machine-capacity constraints

`Production` (decision concept)

One decision row per ProductionRate route; the solver chooses the production quantity.

Property	Type	Identifying?	Notes
`rate`	`ProductionRate`	Yes	One decision variable per machine–product route
`quantity`	float	No	Integer decision variable (`type="int"`), lower bounded by 0

How it works

This section walks through the highlights in production_planning.py.

Import libraries and configure inputs

First, the script imports the Semantics APIs and configures DATA_DIR and the pandas string inference behavior:

from pathlib import Path

import pandas
from pandas import read_csv

from relationalai.semantics import Model, Relationship, data, define, require, sum, where
from relationalai.semantics.reasoners.optimization import Solver, SolverModel

# --------------------------------------------------
# Configure inputs
# --------------------------------------------------

DATA_DIR = Path(__file__).parent / "data"

# Disable pandas inference of string types. This ensures that string columns
# in the CSVs are loaded as object dtype. This is only required when using
# relationalai versions prior to v1.0.
pandas.options.future.infer_string = False

# --------------------------------------------------
# Define semantic model & load data
# --------------------------------------------------

# Create a Semantics model container.
model = Model("production_planning", config=globals().get("config", None))

Define concepts and load CSV data

# Product concept: products with demand and profit per unit.
Product = model.Concept("Product")
Product.id = model.Property("{Product} has {id:int}")
Product.name = model.Property("{Product} has {name:string}")
Product.demand = model.Property("{Product} has {demand:int}")
Product.profit = model.Property("{Product} has {profit:float}")

# Load product data from CSV.
data(read_csv(DATA_DIR / "products.csv")).into(Product, keys=["id"])

# Machine concept: machines with a limited number of available production hours.
Machine = model.Concept("Machine")
Machine.id = model.Property("{Machine} has {id:int}")
Machine.name = model.Property("{Machine} has {name:string}")
Machine.hours_available = model.Property("{Machine} has {hours_available:float}")

# Load machine data from CSV.
data(read_csv(DATA_DIR / "machines.csv")).into(Machine, keys=["id"])

# ProductionRate concept: hours required per unit for each machine-product pair.
Rate = model.Concept("ProductionRate")
Rate.machine = model.Relationship("{ProductionRate} on {machine:Machine}")
Rate.product = model.Relationship("{ProductionRate} for {product:Product}")
Rate.hours_per_unit = model.Property("{ProductionRate} has {hours_per_unit:float}")

# Load production rate data from CSV.
rates_data = data(read_csv(DATA_DIR / "production_rates.csv"))

# Define ProductionRate entities by joining the rate CSV with Machine and Product.
where(
    Machine.id == rates_data.machine_id,
    Product.id == rates_data.product_id
).define(
    Rate.new(machine=Machine, product=Product, hours_per_unit=rates_data.hours_per_unit)
)

Define decision variables, constraints, and objective

# Production decision concept: production quantity for each machine-product pair.
Production = model.Concept("Production")
Production.rate = model.Relationship("{Production} uses {rate:ProductionRate}")
Production.x_quantity = model.Property("{Production} has {quantity:float}")
define(Production.new(rate=Rate))

ProductionRef = Production.ref()

# Scenario parameter (overridden within the scenario loop).
demand_multiplier = 1.0


def build_formulation(s):
    """Register variables, constraints, and objective on the solver model."""
    # Variable: production quantity (integer)
    s.solve_for(
        Production.x_quantity,
        name=[
            "qty",
            Production.rate.machine.name,
            Production.rate.product.name,
        ],
        lower=0,
        type="int",
    )

    # Constraint: machine capacity
    machine_hours = (
        sum(ProductionRef.x_quantity * ProductionRef.rate.hours_per_unit)
        .where(ProductionRef.rate.machine == Machine)
        .per(Machine)
    )
    capacity_limit = require(machine_hours <= Machine.hours_available)
    s.satisfy(capacity_limit)

    # Constraint: meet demand (scaled by demand_multiplier)
    product_qty = sum(ProductionRef.x_quantity).where(ProductionRef.rate.product == Product).per(Product)
    meet_demand = require(product_qty >= Product.demand * demand_multiplier)
    s.satisfy(meet_demand)

    # Objective: maximize total profit
    total_profit = sum(Production.x_quantity * Production.rate.product.profit)
    s.maximize(total_profit)

Solve scenarios and print results

SCENARIO_PARAM = "demand_multiplier"
SCENARIO_VALUES = [0.8, 1.0, 1.1]

scenario_results = []

for scenario_value in SCENARIO_VALUES:
    print(f"\nRunning scenario: {SCENARIO_PARAM} = {scenario_value}")

    # Set scenario parameter value
    demand_multiplier = scenario_value

    # Create fresh SolverModel for each scenario.
    s = SolverModel(model, "cont")
    build_formulation(s)

    solver = Solver("highs")
    s.solve(solver, time_limit_sec=60)

    scenario_results.append(
        {
            "scenario": scenario_value,
            "status": str(s.termination_status),
            "objective": s.objective_value,
        }
    )
    print(f"  Status: {s.termination_status}, Objective: {s.objective_value}")

    # Print production plan from solver results
    var_df = s.variable_values().to_df()
    qty_df = var_df[
        var_df["name"].str.startswith("qty") & (var_df["value"] > 0.001)
    ]
    print(f"\n  Production plan:")
    print(qty_df.to_string(index=False))

# Summary
print("\n" + "=" * 50)
print("Scenario Analysis Summary")
print("=" * 50)
for result in scenario_results:
    print(f"  {result['scenario']}: {result['status']}, obj={result['objective']}")

Customize this template

Change the scenario parameters

This template includes a simple demand sensitivity analysis controlled by demand_multiplier.

Parameter	Type	Values	Description
`demand_multiplier`	numeric	`0.8`, `1.0`, `1.1`	Multiplier applied to all product demands

How to customize the scenarios:

In production_planning.py, edit SCENARIO_VALUES to the multipliers you want to test.

How to interpret results:

If increasing demand_multiplier decreases the objective, demand is forcing production into less-profitable routes.
If changing demand_multiplier does not change the objective, the demand constraints are likely non-binding at those values.

Use your own data

Replace the CSV files under data/.
Keep IDs consistent across files (machine_id / product_id must exist in machines.csv / products.csv).

Extend the model

Add setup costs and binary on/off decisions per route.
Add maximum production limits per product (demand as an upper bound rather than a lower bound).
Add multi-period planning (introduce a Period concept and inventory/transition constraints).

Troubleshooting

Why does authentication/configuration fail?

Run rai init to create/update raiconfig.toml.
If you have multiple profiles, set RAI_PROFILE or switch profiles in your config.

Why does the script fail to connect to the RAI Native App?

Verify the Snowflake account/role/warehouse and rai_app_name are correct in raiconfig.toml.
Ensure the RAI Native App is installed and you have access.

ModuleNotFoundError when running the script

Confirm your virtual environment is activated.
Install the template dependencies from this folder: python -m pip install .

CSV loading fails (missing file or column)

Confirm the CSVs exist under data/ and the filenames match.
Ensure the headers match the expected schema:
- products.csv: id, name, demand, profit
- machines.csv: id, name, hours_available
- production_rates.csv: machine_id, product_id, hours_per_unit

Why do I get Status: INFEASIBLE?

Check that total machine hours are sufficient to meet demand: for each product, at least one route must exist in production_rates.csv.
If you increased demand_multiplier, try lowering it or increasing hours_available.

Why is the production plan empty?

The output filters on value > 0.001 and only prints variables whose names start with qty.
If you suspect near-zero values, print s.variable_values().to_df() without filtering.

Solver fails or returns an unexpected termination status

Try re-running; transient connectivity issues can affect the solve step.
If the solve is slow, reduce problem size (fewer machines/products/routes) or increase time_limit_sec in production_planning.py.

What this template is for

Manufacturers must decide how many units of each product to produce on each machine to maximize profit while meeting customer demand and respecting machine capacity. When market conditions are uncertain, planners need to evaluate how production plans change under different demand scenarios.

This template uses prescriptive reasoning to find the profit-maximizing production plan across a set of machines and products. Each machine has limited available hours, and each machine-product combination has a specific production rate. The model runs multiple demand scenarios (80%, 100%, and 110% of base demand) to show how the optimal plan shifts as demand changes.

The scenario analysis loop demonstrates a powerful pattern for what-if planning. By solving the same model structure under different parameter values, decision-makers can understand the sensitivity of their production strategy to demand fluctuations.

Who this is for

Production planners optimizing machine utilization and product mix
Operations managers evaluating plans under demand uncertainty
Developers learning integer programming and scenario analysis with RelationalAI
Anyone building production scheduling or capacity planning tools

What you’ll build

A multi-machine, multi-product production planning model with integer variables
Machine capacity constraints based on production rates
Demand satisfaction constraints with configurable demand multipliers
A profit maximization objective
A scenario analysis loop comparing results across demand levels

What’s included

production_planning.py — Main script with scenario loop, model definition, and result summaries
data/products.csv — Products with base demand and per-unit profit margins
data/machines.csv — Machines with available hours per planning period
data/production_rates.csv — Hours required per unit for each machine-product combination
pyproject.toml — Python project configuration with dependencies

Prerequisites

Access

A Snowflake account that has the RAI Native App installed.
A Snowflake user with permissions to access the RAI Native App.

Tools

Python >= 3.10

Quickstart

Download ZIP:

curl -O https://docs.relational.ai/templates/zips/v1/production_planning.zip
unzip production_planning.zip
cd production_planning

Create venv:

python -m venv .venv
source .venv/bin/activate
python -m pip install --upgrade pip

Install:
Terminal window
```
python -m pip install .
```
Configure:
Terminal window
```
rai init
```
Run:
Terminal window
```
python production_planning.py
```

Expected output:

Running scenario: demand_multiplier = 0.8
  Status: OPTIMAL, Objective: 14650.0

  Production plan:
           name  value
 qty_Machine_1_Widget_A   80.0
 qty_Machine_1_Widget_C   48.0
 qty_Machine_2_Widget_B   64.0
 qty_Machine_3_Widget_A    2.0
 qty_Machine_3_Widget_B    2.0

Running scenario: demand_multiplier = 1.0
  Status: OPTIMAL, Objective: 15950.0

  Production plan:
           name  value
 qty_Machine_1_Widget_A   80.0
 qty_Machine_1_Widget_C   60.0
 qty_Machine_2_Widget_B   70.0
 qty_Machine_3_Widget_A   20.0
 qty_Machine_3_Widget_B   10.0

Running scenario: demand_multiplier = 1.1
  Status: OPTIMAL, Objective: 16800.0

  Production plan:
           name  value
 qty_Machine_1_Widget_A   80.0
 qty_Machine_1_Widget_B   10.0
 qty_Machine_1_Widget_C   66.0
 qty_Machine_2_Widget_B   70.0
 qty_Machine_3_Widget_A   30.0
 qty_Machine_3_Widget_B   10.0

==================================================
Scenario Analysis Summary
==================================================
  0.8: OPTIMAL, obj=14650.0
  1.0: OPTIMAL, obj=15950.0
  1.1: OPTIMAL, obj=16800.0

Template structure

.
├── README.md
├── pyproject.toml
├── production_planning.py
└── data/
    ├── products.csv
    ├── machines.csv
    └── production_rates.csv

How it works

1. Define the ontology and load data

The model defines products with demand and profit, machines with available hours, and production rates linking each machine-product pair.

Product = Concept("Product", identify_by={"id": Integer})
Product.name = Property(f"{Product} has {String:name}")
Product.demand = Property(f"{Product} has {Integer:demand}")
Product.profit = Property(f"{Product} has {Float:profit}")

Machine = Concept("Machine", identify_by={"id": Integer})
Machine.name = Property(f"{Machine} has {String:name}")
Machine.hours_available = Property(f"{Machine} has {Float:hours_available}")

Rate = Concept("ProductionRate")
Rate.machine = Property(f"{Rate} on {Machine}", short_name="machine")
Rate.product = Property(f"{Rate} for {Product}", short_name="product")
Rate.hours_per_unit = Property(f"{Rate} has {Float:hours_per_unit}")

2. Define decision variables and scenarios

Scenarios are modeled as a Scenario concept with a demand_multiplier property — all scenarios are solved in a single call, not a loop.

Scenario = Concept("Scenario", identify_by={"name": String})
Scenario.demand_multiplier = Property(f"{Scenario} has {Float:demand_multiplier}")

problem = Problem(model, Float)

# Variable indexed by Scenario — one quantity per production rate per scenario
Production.x_quantity = Property(f"{Production} in {Scenario} has {Float:quantity}")
problem.solve_for(
    Production.x_quantity(Scenario, x_qty),
    name=["qty", Scenario.name, Production.rate.machine.name, Production.rate.product.name],
    lower=0, type="int",
)

3. Add constraints

Machine capacity and demand satisfaction constraints are defined per scenario.

# Machine capacity: total production hours <= available hours (per machine, per scenario)
problem.satisfy(model.where(...).require(
    sum(x_qty * Production.rate.hours_per_unit)
    .where(Production.rate.machine == Machine)
    .per(Machine, Scenario)
    <= Machine.hours_available
))

# Meet scaled demand (per product, per scenario)
problem.satisfy(model.where(...).require(
    sum(x_qty).where(Production.rate.product == Product).per(Product, Scenario)
    >= Product.demand * Scenario.demand_multiplier
))

4. Maximize profit

The objective maximizes total profit across all production assignments.

total_profit = sum(Production.x_quantity * Production.rate.product.profit)
problem.maximize(total_profit)

Customize this template

Add more products or machines by extending the CSV files.
Add raw material constraints by introducing material requirements per product and inventory limits.
Model setup times between product changeovers on the same machine.
Extend scenario analysis to vary other parameters like machine availability or profit margins.
Add minimum lot sizes by setting lower bounds on production quantities when a product is produced.

Troubleshooting

Solver returns INFEASIBLE for high demand multipliers

Machine capacity limits how much can be produced. If the demand multiplier is too high, the machines may not have enough hours to meet all demand. Try increasing hours_available in machines.csv or reducing the demand multiplier.

Integer solutions take longer to solve

Integer programming is harder than continuous optimization. For large instances, consider relaxing integer constraints during exploratory analysis by changing type="int" to type="cont", then switch back for final planning.

Connection or authentication errors

Run rai init to configure your Snowflake connection. Verify that the RAI Native App is installed and your user has the required permissions.

ModuleNotFoundError for relationalai

Ensure you activated the virtual environment and ran python -m pip install . to install all dependencies listed in pyproject.toml.

Production Planning

What this template is for

Who this is for

What you’ll build

What’s included

Prerequisites

Access

Tools

Quickstart

Template structure

Sample data

products.csv

machines.csv

production_rates.csv

Model overview

Product

Machine

ProductionRate

Production (decision concept)

How it works

Import libraries and configure inputs

Define concepts and load CSV data

Define decision variables, constraints, and objective

Solve scenarios and print results

Customize this template

Change the scenario parameters

Use your own data

Extend the model

Troubleshooting

What this template is for

Who this is for

What you’ll build

What’s included

Prerequisites

Access

Tools

Quickstart

Template structure

Sample data

products.csv

machines.csv

production_rates.csv

Model overview

Product

Machine

ProductionRate

Production (decision concept)

How it works

Import libraries and configure inputs

Define concepts and load CSV data

Define decision variables, constraints, and objective

Solve scenarios and print results

Customize this template

Change the scenario parameters

Use your own data

Extend the model

Troubleshooting

What this template is for

Who this is for

What you’ll build

What’s included

Prerequisites

Access

Tools

Quickstart

Template structure

How it works

1. Define the ontology and load data

2. Define decision variables and scenarios

3. Add constraints

4. Maximize profit

Customize this template

Troubleshooting

`products.csv`

`machines.csv`

`production_rates.csv`

`Product`

`Machine`

`ProductionRate`

`Production` (decision concept)

`products.csv`

`machines.csv`

`production_rates.csv`

`Product`

`Machine`

`ProductionRate`

`Production` (decision concept)