A two-dimensional cutting stock problem (2DCSP) needs to cut a set of given rectangular items from standard-sized rectangular materials with the objective of minimizing the number of materials used. This problem frequently arises in different manufacturing industries such as glass, wood, paper, plastic, etc. However, the current literatures lack a deterministic method for solving the 2DCSP. However, this study proposes a global method to solve the 2DCSP. It aims to reduce the number of binary variables for the proposed model to speed up the solving time and obtain the optimal solution. Our experiments demonstrate that the proposed method is superior to current reference methods for solving the 2DCSP.

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.

Application of Decision Science in Business and Management is a book where each chapter has been contributed by a different author(s). The chapters introduce and demonstrate a decision-making theory to practice case studies. It demonstrates key results for each sector with diverse real-world case studies. Theory is accompanied by relevant analysis techniques, with a progressive approach building from simple theory to complex and dynamic decisions with multiple data points, including big data, lot of data, etc. Computational techniques, dynamic analysis, probabilistic methods, and mathematical optimization techniques are expertly blended to support analysis of multi-criteria decision-making problems with defined constraints and requirements. The book provides an interface between the main disciplines of engineering/technology and the organizational, administrative, and planning abilities of decision making. It is complementary to other sub-disciplines such as economics, finance, marketing, decision and risk analysis, etc.

The proceedings of the fourth ICMA in 2004 represent a huge contribution to research in this area. Everyone attending the conference was asked to submit their papers electronically which meant that 100 top quality papers from no less that 10 different countries contributed to the theme of the conference.