🏀 NBA Schedule Optimization via Integer Programming

📌 Overview

This project studies the reconstruction and improvement of an NBA regular-season schedule using Integer Programming (IP).

Given a preliminary (fictitious) schedule, the goal is to:

• Reconstruct alternative feasible schedules that preserve league constraints
• Incorporate travel-related constraints (time zones)
• Evaluate improvements in schedule quality using a proxy for travel burden

The project combines data processing, optimization modeling, and performance evaluation to solve a real-world scheduling problem.

---

📂 Data

• games_data.csv: Original schedule dataset containing game dates, home teams, and away teams

---

🧠 Modeling Framework

🔹 Problem 1: Structural Constraint Extraction

From the original schedule, we extract:

• Home game dates for each team
• Away game dates for each team
• Pairwise matchup frequencies

These define the feasible space of all valid schedules.

---

🔹 Problem 2: Feasible Schedule Reconstruction (MILP)

We formulate a Mixed-Integer Linear Program (MILP):

Decision Variable

• x[i,j,d] = 1 if team i hosts team j on date d

Constraints

• Each team plays exactly one game per assigned date
• Home/away dates must match the original schedule
• Matchup frequencies must be preserved

Output

• feasible_schedule_problem2.csv
• feasible_schedule_problem2.pdf

---

🔹 Problem 3: Time-Zone-Constrained Scheduling

We extend the model with travel constraints:

• Each game is associated with a time zone
• Teams cannot play 3 consecutive games with excessive time-zone shifts

Result

• Eliminates infeasible travel sequences
• Maintains full feasibility

Output

• feasible_schedule_problem3.csv
• feasible_schedule_problem3.pdf

---

🔹 Problem 4: Schedule Improvement Analysis

We evaluate schedule quality using a proxy travel metric:

• Total time-zone movement across consecutive games
• Number of "forbidden" travel sequences

Results

• All forbidden sequences are eliminated
• Average travel burden is reduced across teams

Output

• schedule_improvement_summary_problem4.pdf
• schedule_improvement_summary_problem4.csv

---

📈 Results & Insights

• A feasible schedule satisfying all structural constraints exists
• Adding travel constraints does not break feasibility
• Time-zone constraints improve schedule quality:
  • Eliminate extreme travel patterns
  • Reduce cumulative travel burden

This demonstrates how optimization can balance:

• Feasibility
• Operational constraints
• Player welfare considerations

---

🛠️ Tech Stack

• Python (Pandas, NumPy)
• Optimization: PuLP / MILP (CBC Solver)
• Data Processing & Validation

---

📂 Repository Structure

├── games_data.csv                          # Original schedule data
├── feasible_schedule_problem2.csv          # Feasible schedule (P2)
├── feasible_schedule_problem2.pdf
├── feasible_schedule_problem3.csv          # Time-zone constrained schedule (P3)
├── feasible_schedule_problem3.pdf
├── schedule_improvement_summary_problem4.csv  # Travel comparison (P4)
├── schedule_improvement_summary_problem4.pdf
├── NBA_Schedule_Project.ipynb              # Modeling & experiments
├── Optimization_Project_2.pdf              # Final report
└── README.md

---

📄 Report

For full methodology and mathematical formulation, see:

👉 Optimization_Project_2.pdf

---

✨ Key Takeaways

• Integer Programming can reconstruct complex scheduling systems
• Adding realistic constraints improves outcomes without sacrificing feasibility
• Optimization provides a structured way to evaluate trade-offs in large-scale systems

---

👤 Author

Althea He
Columbia University