dantzig-wolfe-decomposition

dantzig-wolfe-decomposition is a skill for Claude Code from hajibabaie/combinatorial-optimization-skills. It costs 141 tokens per session (11,861 once invoked), scanned A, original, MIT.

A method for splitting a large linear or mixed-integer optimization model into smaller independent parts plus a coordinating master model. It is designed for models with groups of variables linked by relatively few shared constraints.

In plain words
What is it for?
Use it to detect block structure, build a Dantzig–Wolfe reformulation, create pricing subproblems, and apply column generation. Typical blocks may represent plants, vehicles, machines, periods, or scenarios.
Why use it?
It can make structured models easier to solve when listing every possible choice as one large model is impractical. It also helps compare the resulting bound with ordinary linear-programming and Lagrangian bounds.

Skill for Claude Code

Written for Claude Code: shipped in a Claude Code plugin.

Part of the combinatorial-optimization plugin — 76 skills shipped together

Good fit Use it to detect block structure, build a Dantzig–Wolfe reformulation, create pricing subproblems, and apply column generation. Typical blocks may represent plants, vehicles, machines, periods, or scenarios.

Compare 6 skills from other repositories ↓
Install with agentmods
npx agentmods add skills/hajibabaie/combinatorial-optimization-skills/dantzig-wolfe-decomposition
Install

Getting it into your agent

One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.

Any agent
npx skills add hajibabaie/combinatorial-optimization-skills --skill dantzig-wolfe-decomposition
Clone the repo
git clone --depth 1 https://github.com/hajibabaie/combinatorial-optimization-skills

Made for: Claude Code.

Or install combinatorial-optimization, the plugin that ships this one along with the rest of its 76 skills.

Wrote this? Show the measurements

A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.

agentmods badge for dantzig-wolfe-decomposition

README.md
[![agentmods](https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/dantzig-wolfe-decomposition/github.svg)](https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/dantzig-wolfe-decomposition)
Your own site
<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/dantzig-wolfe-decomposition"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/dantzig-wolfe-decomposition/github.svg" alt="Measured on agentmods" height="20"></a>

Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.

agentmods 80×15 button for dantzig-wolfe-decomposition

Your own site · 80×15
<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/dantzig-wolfe-decomposition"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/dantzig-wolfe-decomposition.svg" alt="Reviewed on agentmods" width="80" height="20"></a>
Per session 141 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 11,861 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe.
Origin original No closer match found in the catalogue.
Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

ModelPer sessionOnce invoked
Fable 5.1 $0.00141 $0.11861
Opus 5 $0.00071 $0.05930
Sonnet 5 $0.00028 $0.02372
Haiku 4.5 $0.00014 $0.01186

Measured 9d ago against content hash 1c1ea65aba42, method: parsed. Prices are Anthropic first-party input rates as of 2026-09-09, from the pricing page.

Security

Grade A, and why

dantzig-wolfe-decomposition scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 9d ago.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

skills/dantzig-wolfe-decomposition/SKILL.md · 707 lines

How it starts

The opening of the file, as written. The whole thing — 707 lines — stays where its author put it; the contents beside it link to each section on GitHub.

Dantzig-Wolfe Decomposition

You are an expert in Dantzig-Wolfe (DW) decomposition for linear and mixed-integer programs. This skill covers detecting block-angular structure in a constraint matrix, reformulating the original (compact) model into a master problem with convexity constraints plus independent pricing subproblems, solving the reformulation by column generation, and interpreting the resulting bound against the LP relaxation, the Lagrangian dual, and the integer optimum. Use the framework below to decide whether a model is worth decomposing, to execute the reformulation correctly, and to verify the bound relationships on the user's instance.

Initial Assessment

Establish the following before reformulating anything:

  • Structure. Which constraint rows couple otherwise-independent variable groups? Ask the user to name the natural blocks (plants, vehicles, machines, periods, scenarios). If they cannot, run structure detection on the constraint matrix (section below).
  • Linking fraction. Count linking rows m0 versus total rows. DW pays off when m0 is small relative to the block rows — a useful rule of thumb is linking rows below 10-20% of all rows.
  • Problem class. LP or MIP? If MIP, locate the integrality: integer variables inside blocks make the DW bound potentially stronger than the LP bound; integrality that lives only in the linking rows gains nothing from convexification.
  • Block inventory. Number of blocks K, variables per block, and whether the blocks are identical (same costs, same constraint data). Identical blocks call for the aggregated master, which removes symmetry.
  • Pricing tractability. What does one block look like in isolation? A knapsack, a shortest path, a small assignment, a small MIP? The whole method stands or falls on solving the pricing problem quickly and repeatedly.
  • Boundedness. Are the block polyhedra bounded? If not, the implementation must handle extreme rays, not just extreme points.
  • Goal. A tighter dual bound, a faster LP solve on a huge structured model, or an integer optimum? The first two end with column generation; the third requires branch-and-price (hand off to the column-generation skill).
  • Baseline. Solve the compact model (or its LP relaxation) first. Record z_LP, the MIP gap, and the time. Without this baseline you cannot say whether DW helped.
  • Solver access. Gurobi license for master and pricing? If not, plan for HiGHS as the master LP solver and GCG/SCIP for an automatic end-to-end alternative.
  • Stopping policy. Run column generation to proven optimality, or stop early on a Lagrangian-bound gap? Agree on the tolerance up front.
  • Time budget. Per-iteration cost is one RMP LP plus K pricing solves. Estimate iterations in the tens-to-hundreds range and check the budget supports that.

Read the full file on GitHub · 707 lines

Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

  1. 9d ago First seen · 707 lines · 141 tokens per session scan A 1c1ea65aba42

Subscribe to this mod's changes

dantzig-wolfe-decomposition is a skill published in the GitHub repository hajibabaie/combinatorial-optimization-skills (7 stars, last pushed 2mo ago), licensed MIT. It adds 141 tokens to every session and 11,861 once invoked, about $0.0007 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-31.

Related

Other skills, from other repositories

learn-from-fix

Capture Elixir/Ecto/LiveView lessons and Hex API rules. Use after corrections or when asked to document learning, record a lesson, prevent a fixed mistake, or remember package guidance with --library.

oliver-kriska/claude-elixir-phoenix · 46 tokens

phx-deps-audit

Audit Hex deps for supply-chain security risk — bidi chars, compile-time exec, maintainer changes, typosquats, CVEs. Use after mix deps.update, when checking if a package upgrade is safe, or reviewing mix.lock PR diffs.

oliver-kriska/claude-elixir-phoenix · 58 tokens

promote

Generate X/Twitter release promotion posts with ASCII tables and CodeSnap rendering. Use when writing release posts, promotion tweets, plugin announcements, or preparing social media content for new versions.

oliver-kriska/claude-elixir-phoenix · 39 tokens

release

CONTRIBUTOR TOOL - Cut a plugin release: bump plugin.json version, finalize CHANGELOG, update README if needed, gate on make ci, commit, tag vX.Y.Z, and create the GitHub release. Use when shipping a new plugin version. NOT distributed.

oliver-kriska/claude-elixir-phoenix · 60 tokens

session-deep-dive

Deep qualitative analysis of high-signal sessions. Spawns subagents with v2 template, synthesizes patterns, compares against known findings. Use after /session-scan.

oliver-kriska/claude-elixir-phoenix · 40 tokens

catchup

Summarize and review what changed while you were away. Use after a weekend, vacation, or flight to check missed PRs, git commits, Linear tickets, and meetings — one prioritized brief, not a firehose.

oliver-kriska/claude-elixir-phoenix · 48 tokens