1. Introduction (3 min) – What Kind of Problems Can MIP Solve?

• MIP is widely used in scheduling, logistics, and operations research.
• Examples of real-world problems: workforce scheduling, vehicle routing, and conference scheduling.
• Why are these problems hard? The explosion of possible solutions in combinatorial optimization.

2. Why Are These Problems Difficult? (2 min) – The Challenge of Combinatorial Optimization

• Theoretical complexity: Why brute-force search is infeasible.
• How solvers like HiGHS approach the problem efficiently:
  • Branch-and-Bound: How it systematically narrows down the search space.
  • Cutting Planes & Presolve Techniques: Reducing problem size before solving.
  • Heuristics vs. Exact Solutions: Trade-offs in computation time.

3. Introduction to Pyomo & HiGHS (4 min) – The Optimization Toolkit

• Pyomo: A structured way to define optimization models in Python.
• HiGHS: A high-performance solver for linear and mixed-integer problems.
• How they work together: Model in Pyomo → Solve with HiGHS → Interpret results.

4. Conference Scheduling (5 min) – A Practical Example

• Formulating the problem as a MIP model:
  • Decision variables: Assigning talks to rooms and time slots.
  • Constraints: Speaker availability, room capacities, topic grouping.
  • Objective function: Maximizing session coherence and fairness.
• Broad overview of the Python implementation:
  • Writing the model in Pyomo.
  • Solving it using HiGHS.
  • Evaluating the solution.

5. Conclusion & Wrap-up (1 min) – Key Takeaways

• Why Pyomo and HiGHS? Flexibility, efficiency, and scalability.
• Where to go next: Learning resources and real-world applications beyond scheduling.