Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation

Algorithms for 3D guillotine cutting problems: Unbounded knapsack, cutting stock and strip packing

We present algorithms for the following three-dimensional (3D) guillotine cutting problems: Unbounded Knapsack, Cutting Stock and Strip Packing. We consider the case where the items have fixed orientation and the case where orthogonal rotations around all axes are allowed. For the Unbounded 3D Knapsack problem, we extend the recurrence formula proposed by Beasley for the Rectangular Knapsack Pr...

A Comparative Study of Exact Algorithms for the Two Dimensional Strip Packing Problem

In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...

Column generation and sequential heuristic procedure for solving an irregular shape cutting stock problem

Research addressing two-dimensional irregular shape packing has largely focused on the strip packing variant of the problem. However, it can be argued that this is a simplification. Materials from which pieces are required to be cut will ultimately have a fixed length either due to the physical dimensions of the material or through constraints on the cutting machinery. Hence, in order to cut al...

A Value-Correction Construction Heuristic for the Two-Dimensional Cutting Stock Problem with Variable Sheet Size

Cutting and packing problems occur in many real-world applications such as industrial glass, paper or steel cutting, container loading and VLSI design [1]. In this work we consider in particular the two-dimensional cutting stock problem with variable sheet size (2CSV) in which we are given a set of nE rectangular element types E = {1, . . . , nE}, each i ∈ E specified by a height hi ∈ N, a widt...

 Abstract: Packing rectangular shapes into a rectangular space is one of the most important discussions on Cutting & Packing problems (C;P) such as: cutting problem, bin-packing problem and distributor's pallet loading problem, etc. Assume a set of rectangular pieces with specific lengths, widths and utility values. Also assume a rectangular packing space with specific width and length. The obj...