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mip-modeling-expert

Formulate mixed-integer programming models with indicator variables and Big-M constraints.

1|Updated Oct 1, 2025
Search Tags:#optimization#MIP#linearization#indicator-variables#Big-M#SOS#piecewise-linear
One-click install
npx skills add https://github.com/sverzijl/planning_latest --skill mip-modeling-expert
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: mip-modeling-expert
Source: https://github.com/sverzijl/planning_latest/tree/main/.claude/skills/mip-modeling-expert
Command: npx skills add https://github.com/sverzijl/planning_latest --skill mip-modeling-expert

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill includes references (resource) components.

What problem does it solve?

The MIP Modeling Expert skill provides practical, field-tested techniques to transform complex optimization problems into solvable mixed-integer programs. It focuses on handling discontinuous variables, logical constraints, and nonlinear terms via linearization and modeling tricks.

Core Features & Use Cases

  • Indicator variables and discontinous variable modeling to enforce zero-or-bounded ranges.
  • Big-M, SOS1/SOS2, and logical constraints to encode either-or and conditional relationships.
  • Piecewise linear approximations and product linearization for nonlinear terms, enabling exact or tightly bounded MILP solutions.
  • Guidance examples across production, logistics, facility location, and budget problems with actionable formulations for Gurobi/CPLEX.

Quick Start

Use the mip-modeling-expert skill to generate a minimal MIP formulation for a binary-discontinuous variable example, including a small dataset and complete constraints, then derive a tight Big-M bound.

Frequently Asked Questions about mip-modeling-expert

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I formulate logical constraints in mixed-integer programming?▼

Piecewise linear approximations model nonlinear terms in mixed-integer programming by transforming product linearization and discontinuous variable relationships into tightly bounded linear constraints.

How do I derive tight bounds for a Big-M formulation?▼

Deriving tight Big-M bounds requires analyzing the maximum and minimum feasible values of your discontinuous variables to ensure solver efficiency and prevent unbounded or slow branch-and-bound trees.

Can I use indicator variables to enforce zero-or-bounded ranges in Gurobi or CPLEX?▼

Yes, indicator variables can enforce zero-or-bounded ranges in major MILP solvers like Gurobi and CPLEX by triggering variable bounds conditionally based on a binary activation state.

What's the best way to model discontinuous variables in production scheduling problems?▼

The best way to model discontinuous variables in production scheduling is applying SOS1 or SOS2 constraints alongside piecewise linear approximations to handle complex operational either-or decisions.

When should I use SOS constraints instead of Big-M in a facility location model?▼

Use SOS constraints instead of Big-M in facility location models when you need to strictly enforce mutually exclusive choices without relying on large constants that can degrade solver numerical stability.

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