# Column Generation for the Cutting Stock Problem

## 35 Pages, Grade: 1,3

Abstract or Introduction

The Cutting Stock Problem (CSP) appears when a material has to be cut into smaller pieces and occurs in many branches of industry. On the one hand, the CSP belongs to the earliest studied problems through methods of Operational Research and on the other to the most intensively studied problems in combinatorial optimization.

In the one-dimensional Cutting Stock Problem (1DCSP), there are typically identical pieces of a single standard length, called rolls, that need to be cut into smaller pieces lengthwise. Examples, where the cutting process is performed in one single dimension, can be found in the steel industry and the paper industry . The two-dimensional CSP (2DCSP) is classified into cutting of regular and irregular shapes and is often found in clothing and shoe-leather industries. A real-world application of a three-dimensional CSP (3DCSP) lies in the production of mattresses, where rubber blocks are cut into different types of orthogonal rectangular prisms.

Methods of finding an optimal solution exist for the 1DCSP. Often in large problem instances, the required time for finding an optimal solution proliferates, and heuristics may turn out to be the more sensible option in this case. Nowadays, there are countless different ways to find acceptable solutions in a fast manner of time, among others, the column generation approach, which is the central component of the present work.

This work is organized as follows. In Chapter 2, a brief overview of different formulations for the CSP is given. Furthermore, some known extensions of the classic CSP are presented, e.g., raw material, that consists of various sizes at the same time.

CSP has many relatives, the closest is the Bin Packing Problem (BPP), where items are packed into bins as efficiently as possible. The third chapter shows the column generation technique for solving the CSP and provides the connection between a solution for the relaxed problem and an integer solution. In Chapter 4, different test instances of the CSP are compared using a column generation implementation solved in three different MIP solvers. The conclusion is provided in Chapter 5.

Details

Title
Column Generation for the Cutting Stock Problem
College
University of Kaiserslautern
1,3
Author
Year
2020
Pages
35
Catalog Number
V1061428
ISBN (eBook)
9783346475831
ISBN (Book)
9783346475848
Language
English
Tags
column, generation, cutting, stock, problem
Quote paper
Marvin Caspar (Author), 2020, Column Generation for the Cutting Stock Problem, Munich, GRIN Verlag, https://www.grin.com/document/1061428

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