In this paper, an integer programming model for two-dimensional cutting stock problems is proposed. In the problems addressed, it is intended to cut a set of small rectangular items of given sizes from a set of larger rectangular plates in such a way that the total number of used plates is minimized. The two-stage and three-stage, exact and non-exact, problems are considered. Other issues are a...

Abstract In this paper, we study the packing optimization problem of square plates under conditions that cutting mode is guillotine cut, number stages cannot exceed 3, and order sequence not considered. Because it difficult to determine constraint in process stacking items into stacks, divide nonlinear integer programming model two establish: one stage stacks followed by splicing them stripes, ...

A method for separation and purification of plant hormones auxin and abscisic acid based on mixed mode reversed-phase anion-exchange solid phase extraction and two-dimensional HPLC was developed. Two-dimensional HPLC in "heart cutting" mode was very efficient in the purification of these two hormones. Its purification power is high enough to allow reliable on-line quantification of both hormone...

We survey the main formulations and solution methods for two-dimensional orthogonal cutting packing problems, where both items bins are rectangles. focus on exact relaxations four problems from literature: finding a with minimum height, into number of bins, maximum value, determining existence feasible packing.

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...