Demand prediction and Optimization with scikit-learn & Amplpy

Description: In this notebook, we will:

1. Train a linear regression model to predict product demand based on price and marketing spend.

2. Use the predicted demand in a simple optimization model with AMPL to determine the optimal production quantity that maximizes profit under given constraints.

Tags: amplpy, machine-learning, scikit-learn, gurobi

Notebook author: Marcos Dominguez Velad <marcos@ampl.com>

Model author: N/A

# Install dependencies
%pip install -q amplpy numpy scikit-learn

# Google Colab & Kaggle integration
from amplpy import AMPL, ampl_notebook

ampl = ampl_notebook(
    modules=["gurobi"],  # modules to install
    license_uuid="default",  # license to use
)  # instantiate AMPL object and register magics

Train the Demand Prediction Model

We’ll start by using historical data to train a linear regression model that predicts demand based on price and marketing spend.

from sklearn.linear_model import LinearRegression
import numpy as np

# Historical dataset: [price, marketing spend] → demand
X = np.array([[10, 1000], [12, 1500], [14, 800], [13, 1200], [11, 1100]])
y = np.array([120, 115, 90, 110, 118])  # Observed demand

# Fit linear regression model
model = LinearRegression()
model.fit(X, y)

LinearRegression()

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Predict demand for a new case

Now we use the trained model to predict the demand for a product given a specific price and marketing spend.

# New input values
price = 13
marketing_spend = 1300

# Predict demand
predicted_demand = model.predict([[price, marketing_spend]])[0]
print(f"Predicted demand: {predicted_demand:.2f}")

Predicted demand: 107.77

Formulate the Optimization Problem in AMPL

We’ll use AMPL to define and solve a profit-maximizing problem:

• Objective: Maximize profit = (price - unit cost) × quantity

• Subject to:

  • Quantity must not exceed capacity

  • Quantity must not exceed predicted demand

%%writefile demand.mod
param predicted_demand;
param unit_cost;
param price;
param capacity;

var quantity >= 0, <= capacity;

maximize profit: (price - unit_cost) * quantity;

s.t. DemandLimit: quantity <= predicted_demand;

Overwriting demand.mod

Load data and Solve

We assign values to model parameters and solve the optimization problem using the Gurobi solver.

# Define optimization model in AMPL
ampl.read("demand.mod")

unit_cost = 5
capacity = 150

# Load data
ampl.param["price"] = price
ampl.param["unit_cost"] = unit_cost
ampl.param["capacity"] = capacity
ampl.param["predicted_demand"] = predicted_demand

# Solve the model
ampl.solve(solver="gurobi")
assert ampl.solve_result == "solved", ampl.solve_result

Gurobi 12.0.1:Gurobi 12.0.1: optimal solution; objective 862.1837838
0 simplex iterations

Display results

Let’s retrieve and print the optimal production quantity and the expected profit.

# Get results from AMPL
quantity = ampl.var["quantity"].value()
profit = ampl.obj["profit"].value()

print(f"Optimal quantity to produce: {quantity:.2f}")
print(f"Expected profit: {profit:.2f}")

Optimal quantity to produce: 107.77
Expected profit: 862.18

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Explore our open-source model repository:
🔗 colab.ampl.com

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