Blog
Guides & worked examples
Notes on mathematical optimization, linear and mixed-integer programming, and using MCP servers to give AI agents provably optimal answers.
July 30, 2026
Committed Use Discount Planning: Forecast-Driven vs Usage-Based
Usage-based CUD buying sizes commitments from your past and hedges the future. Forecast-driven planning optimizes for the demand you already know — and when your demand is contractual, that's not a guess.
July 16, 2026
How Much CUD Should You Buy?
Commit too much and you pay for idle capacity; commit too little and you overpay on-demand. Coverage, utilization, and break-even are how you find the line between them.
July 14, 2026
1-Year vs 3-Year Committed Use Discounts
A 3-year commitment is cheaper per unit than a 1-year one — but it's a bigger bet on demand you can't yet see. How to think about the term trade-off, and where break-even comes in.
July 6, 2026
Why AI Agents Need Deterministic Solvers
Ask a large language model the same question twice and you can get two different answers. That's fine for conversation, and unacceptable for scheduling and cost decisions — here's why.
July 5, 2026
Home Energy Management Optimization: A Worked Example
An EV charging deadline, a home battery, dynamic hourly tariffs, and a heat pump's thermal inertia — walked through as the optimization problem behind Solvicus's home-energy-management use case.
July 4, 2026
Crop Rotation Scheduling: A Worked Example
24 fields, a 3-year Fabaceae break rule, and a 5-year price forecast — walked through as the mixed-integer program behind Solvicus's crop-rotation use case.
July 3, 2026
GCP Committed Use Discount Optimization: A Worked Example
250 customer contracts, three e2 machine sizes, and a CUD renewal decision — walked through as the mixed-integer program Solvicus actually solves to pick your commitments.
July 1, 2026
Staff Scheduling Optimization: A Worked Example
A 15-physician practice, room constraints, and labor-law rest periods — walked through as a mixed-integer program to show why spreadsheets and manual rostering break down.
June 19, 2026
Linear Programming vs. Mixed-Integer Programming
Continuous variables get you linear programming. Add yes/no decisions and whole-unit counts, and you need mixed-integer programming instead. Here's the difference.
June 6, 2026
What Is Mathematical Optimization?
Variables, objectives, and constraints: the three ingredients behind every optimization problem, and why the answer they produce is provably optimal — not a best guess.