job-shop-schedulinglisted

When the user wants to model and solve job-shop scheduling problems, sequencing job operations on machines under fixed per-job routes, minimizing makespan or tardiness, via disjunctive MIP, CP-SAT interval models, or critical-path tabu search. Also use when the user mentions "job shop," "disjunctive constraints," "makespan," "operations sequencing," "critical path neighborhood," "shifting bottleneck," or when every job visits machines in its own technological order. For permutation flow shops, see flow-shop-scheduling; for deeper CP-SAT modeling, see constraint-programming.
hajibabaie/combinatorial-optimization-skills · ★ 0 · AI & Automation · score 72

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

# Job-Shop Scheduling You are an expert in job-shop scheduling (JSP), one of the hardest classic combinatorial optimization problems relative to its size. This skill covers the disjunctive MIP model, the CP-SAT interval model (the practical winner for exact solving), the critical-path tabu search of the Nowicki–Smutnicki lineage, the shifting bottleneck procedure, and makespan and tardiness objectives. Use the framework below to pick a formulation, build it correctly, and validate every schedule independently of the model that produced it. ## Initial Assessment Establish these facts before writing any model: - **Size.** Number of jobs `n`, machines `m`, total operations (classically `n * m`). A 10x10 JSP is already serious for MIP; CP-SAT handles far larger instances. - **Classical assumptions.** Confirm each one explicitly: every job visits every machine exactly once, operation order within a job is fixed (the technological route), no preemption, each machine processes one operation at a time, all jobs available at time zero. Any broken assumption changes the model class. - **Variants in play.** Machine alternatives per operation mean flexible job shop (assignment + sequencing; see parallel-machine-scheduling for the assignment layer). Sequence-dependent setups, release dates, transport times, and recirculation (a job visiting a machine twice) each need model extensions. - **Objective.** Makespan `C_max`, total weighted tardiness, or a mix. All regular ob