Column Generation for the Cutting Stock Problem

Language: English

Published by GRIN Verlag Okt 2021, 2021

3346475840 / 9783346475848

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This item is printed on demand - Print on Demand Titel. Neuware -Seminar paper from the year 2020 in the subject Business economics - Operations Research, grade: 1,3, University of Kaiserslautern, language: English, abstract: 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.GRIN Publishing GmbH, Waltherstraße 23, 80337 München 40 pp. Englisch.…

Seller Inventory # 9783346475848

Title
Column Generation for the Cutting Stock Problem
Author
Marvin Caspar
Publisher
GRIN Verlag Okt 2021
Publication year
2021
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3346475840
ISBN 13
9783346475848
Item weight
73 grams
Dimensions
210x148x4 mm

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