Learning Objectives

• Apply optimization techniques
• Create decision support tools
• Implement recommendation systems

python
Run Inline
from scipy.optimize import minimize_scalar
import numpy as np
# Demand function from regression (example: price -> demand)
demand_coef = {'intercept': 1000, 'price_coef': -5, 'elasticity': -1.2}
def profit(price):
    """Calculate expected profit at given price."""
    demand = demand_coef['intercept'] + demand_coef['price_coef'] * price
    cost = 50  # unit cost
    return -(price - cost) * demand  # Negative for minimization
# Find optimal price
result = minimize_scalar(profit, bounds=(50, 200), method='bounded')
optimal_price = result.x
optimal_profit = -result.fun
print(f"Optimal price: ${optimal_price:.2f}")
print(f"Expected profit: ${optimal_profit:.0f}")

Q1: What is prescriptive analytics?

Recommends actions to achieve desired outcomes. Uses optimization, simulation, decision rules. Answers: "What should we do?" instead of "What will happen?" Q2: What is linear programming?

Optimization with linear objective function and linear constraints. Used for: resource allocation, product mix, logistics, scheduling. Solver: scipy.optimize.linprog, pulp, ortools. Q3: What is a recommendation system?

Suggests items to users. Collaborative filtering (user-item interactions), Content-based (item features), Hybrid. Evaluation: precision@k, recall@k, NDCG. Q4: What is A/B testing for optimization?

Compare two versions (A=current, B=new). Measure metrics (conversion, revenue). Use statistical significance to decide if B is better. Sample size matters. Q5: What is simulation?

Model real-world scenarios with random variables. Monte Carlo simulation runs many iterations to estimate outcomes and risks. Useful when analytical solution is complex. Q6: Simple recommendation engine:

python
Run Inline
# Content-based recommendation
from sklearn.feature_extraction.text import TfidfVectorizer
from sklearn.metrics.pairwise import cosine_similarity

# Item descriptions
items = ['Laptop with SSD', 'Gaming mouse', 'USB-C hub', 'Mechanical keyboard']
tfidf = TfidfVectorizer()
matrix = tfidf.fit_transform(items)
similarities = cosine_similarity(matrix)

# Find most similar to item 0 (laptop)
recommended = similarities[0].argsort()[-3:][::-1]
print(f"Items similar to laptop: {[items[i] for i in recommended if i != 0]}")