Solving One-Dimensional Cutting Stock Problems Exactly with a Cutting Plane Algorithm

Abstract

The one-dimensional cutting stock problem (CSP) is as follows: Given an unlimited number of pieces of identical stock material of length L the task is to cut b _i pieces of length ℓ _i for i ∈ I = {1, …, m} while minimizing the number of stock material pieces needed. Let ℓ = (ℓ₁, …, ℓ _m )^T and b = (b ₁, …, b _m )^T. Without loss of generality, let L ≥ ℓ₁ > … > ℓ _m > 0 and b _i > 0 for i ∈ I