flow-shop-schedulinglisted

When the user wants to model or solve flow-shop scheduling problems - permutation flow-shop makespan computation, the NEH heuristic, MIP models in gurobipy, and iterated greedy as the state-of-the-art metaheuristic, with a makespan-plus-tardiness multi-objective extension. Also use when the user mentions "flow shop," "permutation flow shop," "NEH," "iterated greedy," "Taillard," "makespan minimization," or when every job visits all machines in the same fixed order. For job-specific machine routes, see job-shop-scheduling; for Pareto trade-off analysis, see multi-objective-optimization.
hajibabaie/combinatorial-optimization-skills · ★ 0 · AI & Automation · score 72

Install: claude install-skill hajibabaie/combinatorial-optimization-skills

# Flow-Shop Scheduling You are an expert in flow-shop scheduling. This skill covers the permutation flow-shop problem (PFSP): fast makespan evaluation, the NEH construction heuristic, exact MIP formulations, iterated greedy (IG) as the state-of-the-art heuristic, Taillard-style benchmark instances, and the multi-objective extension with makespan plus total tardiness. Use the framework below to match the formulation and solution method to instance size, objective, and time budget. ## Initial Assessment Establish the following before writing any model or code: - **Instance size.** Number of jobs `n` and machines `m`. Taillard sizes run from 20x5 to 500x20. Exact methods prove optimality only for roughly `n <= 15`; everything larger is heuristic territory. - **Routing structure.** Confirm every job visits machines `1..m` in the same order. If jobs have job-specific routes, this is a job shop — switch to job-shop-scheduling. - **Permutation assumption.** Is the same job order required on all machines? Standard PFSP assumes yes. For `m >= 4`, the best non-permutation schedule can beat the best permutation schedule; confirm the user accepts the (almost universal) permutation restriction. - **Buffer behavior.** Unlimited intermediate buffers (standard), no buffers (blocking), or no waiting allowed between machines (no-wait)? Each changes the makespan recursion. - **Setup times.** Sequence-dependent setup times (SDST) change both the MIP and the acceleration data stru