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.
npx skills add hajibabaie/combinatorial-optimization-skills --skill lot-sizinggit clone --depth 1 https://github.com/hajibabaie/combinatorial-optimization-skillsWrote 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.
[](https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/lot-sizing)<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/lot-sizing"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/lot-sizing/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.
<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/lot-sizing"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/lot-sizing.svg" alt="Reviewed on agentmods" width="80" height="20"></a>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.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00140 | $0.11166 |
| Opus 5 | $0.00070 | $0.05583 |
| Sonnet 5 | $0.00028 | $0.02233 |
| Haiku 4.5 | $0.00014 | $0.01117 |
Grade A, and why
lot-sizing 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.
How it starts
The opening of the file, as written. The whole thing — 663 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Lot Sizing
You are an expert in dynamic lot-sizing models for production planning. This skill covers the uncapacitated single-item problem (ULS) solved exactly by the Wagner-Whitin dynamic program, the multi-item capacitated lot-sizing problem (CLSP) with setup costs and setup times, strong reformulations (facility-location, (l,S) valid inequalities), the big-bucket vs small-bucket model families, and fix-and-optimize matheuristics for large instances. Use the framework below to classify the variant, pick the right formulation strength, and deliver a validated production plan with a defensible optimality gap.
Initial Assessment
Establish these facts before formulating anything:
- Capacity. Is per-period production capacity binding? Uncapacitated single-item problems are polynomially solvable; capacity makes even the single-item case NP-hard.
- Number of items and periods. N items × T periods sets the binary count (N·T setup variables). N·T ≤ a few thousand is comfortable MIP territory; beyond that plan for matheuristics.
- Bucket size. Are periods long (weeks/months, many setups per period — big bucket) or short (shifts/hours, at most one or two products per period — small bucket)? This decides the model family before any code is written.
- Setup structure. Setup costs only, or also setup times that consume capacity? Setup times change the complexity class of the feasibility question. Ask about setup carryover across periods and sequence-dependent setups.
- Cost structure. Time-varying or constant setup/holding/production costs? Constant unit production cost can be dropped from the objective (total production equals total demand when backlog is forbidden).
- Backlogging and lost sales. Hard demand satisfaction, backlog at a cost, or lost sales? This changes the flow-balance constraints and the validity of zero-inventory-ordering arguments.
- Lot-size restrictions. Minimum lot sizes, batch multiples, or all-or-nothing production invalidate the Wagner-Whitin structure and need extra integer variables.
- Demand certainty. Deterministic forecast, or stochastic demand needing safety stock / scenario models? A deterministic model re-solved in a rolling horizon is the common practical pattern.
- Horizon usage. One-shot plan or rolling horizon? Rolling horizons need end-of-horizon inventory rules and frozen periods to control nervousness.
- Quality requirement and time budget. Proven optimality (MIP with strong formulation), small gap in minutes (matheuristic), or instant answer (DP / construction heuristic)?
- Solver availability. Gurobi license, or open-source only? The DP and the metaheuristic below need only numpy; the MIP sections need a MILP solver.
- Data format. Demand matrix orientation (items × periods), units of capacity (hours vs pieces), and whether quantities must be integral (usually production quantities may stay continuous).
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.
- 9d ago First seen · 663 lines · 140 tokens per session scan A 589db26aef80
lot-sizing is a skill published in the GitHub repository hajibabaie/combinatorial-optimization-skills (7 stars, last pushed 2mo ago), licensed MIT. It adds 140 tokens to every session and 11,166 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.
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