General Math Modeling Workflow

Problem it addresses

Math modeling competition tasks are rarely one clean formula. They are multi-part, constraint-heavy, data-driven problems where speeds, time windows, capacity, penalties, and carbon factors hide in the statement and Excel or CSV files. The next part often adds new constraints on top of the previous one. A direct solve attempt can easily miss parameters, violate constraints, or produce results that cannot be reviewed.

How the workflow works

The skill turns the solution process into inspectable stages:

• Understand the problem: read the statement and data files, then separate sub-problems, objectives, constraints, and parameters.
• Design the architecture: choose Mixed Integer Programming, heuristics, or dynamic programming; plan data loading, initial construction, 2-opt, constraint checks, and cost calculation.
• Implement the solver: use Python, pandas, and numpy to build distance matrices and cost functions for time-dependent travel, U-shaped energy use, soft time windows, and carbon pricing.
• Validate and analyze: find violating routes, apply targeted fixes, and export problemX_solver.py, problemX_result.json, problemX_result.txt, and figures.

It emphasizes multi-problem progression: Problem N+1 starts from the Problem N baseline, adds new constraints incrementally, and compares results across parts.

Boundaries

It fits well for vehicle routing, cost optimization, and multi-constraint planning where metrics can be quantified. For proof-heavy, ambiguous, or data-free competition problems, assumptions and scoring criteria need manual clarification.