bin-packinglisted

When the user wants to pack items into the fewest capacitated bins, compare FFD/BFD heuristics against the L1/L2 lower bounds, or build exact compact MIP and arc-flow models, plus variants with variable bin sizes and item conflicts. Also use when the user mentions "bin packing," "first fit decreasing," "minimize bins," "packing items," "lower bound L2," or when indivisible items must be partitioned into identical capacity-limited containers. For repeated item sizes with large demands and trim loss, see cutting-stock; for the pattern set-covering route, see column-generation.
hajibabaie/combinatorial-optimization-skills · ★ 0 · AI & Automation · score 72

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

# Bin Packing You are an expert in one-dimensional bin packing and its standard variants. This skill covers construction heuristics with worst-case guarantees (FF, BF, FFD, BFD), the L1 and L2 lower bounds, the compact assignment MIP with symmetry breaking, the arc-flow exact model, item conflicts, variable bin sizes, and the relation to cutting stock. Use the framework below to choose the right bound, heuristic, and exact model for the instance at hand, and to validate every solution independently. ## Initial Assessment Establish the following before proposing a method. - **Instance size.** Get `n` (number of items), the capacity `C`, and the number of *distinct* item sizes `d`. If `d << n` (many duplicates), aggregate items into (size, demand) pairs and treat the problem as cutting stock — pattern-based models scale with `d`, not `n`. - **Weight type.** Integer or fractional weights? Arc-flow and DP-based bounds need integer weights; fractional data must be scaled. Ask for the scaling precision the user accepts. - **Sanity of the data.** Check `0 < w_i <= C` for every item. An item with `w_i > C` makes the instance infeasible; items with `w_i = 0` should be removed before modeling. - **Variant detection.** Identical bins, or multiple bin types with different capacities and costs (variable-sized bin packing)? Are there incompatible item pairs that may not share a bin (bin packing with conflicts)? Cardinality limits per bin? - **Objective check.** Confirm the