Hadj Salem

Abstract
In this paper, we consider the two-dimensional Variable-Sized Cutting Stock Problem (2D-VSCSP) with guillotine constraint, applied to the home textile industry. This is a challenging class of real-world prob-lems where, given a set of predefined widths of fabric rolls and a set of piece types, the goal is to de-cide the widths and lengths of the fabric rolls to be produced, and to generate the cutting patterns to cut all demanded pieces. Each piece type considered has a rectangular shape with a specific width and length and a fixed demand to be respected. The main objective function is to minimize the total amount of the textile materials produced/cut to satisfy the demand. According to Wascher, Hau ss ner, & Schu-mann (2007), the addressed problem is a Cutting Stock Problem (CSP), as the demand for each item is greater than one. However, in the real-world application at stake, the demand for each item type is not very high (below ten for all item types). Therefore, addressing the problem as a Bin-Packing Problem (BPP), in which all items are considered to be different and have a unitary demand, was a possibility. For this reason, two approaches to solve the problems were devised, implemented, and tested: (1) a CSP model, based on the well-known Lodi and Monaci (2003) model (3 variants), and (2) an original BPP-based model. Our research shows that, for this level of demand, the new BPP model is more competitive than CSP models. We analyzed these different models and described their characteristics, namely the size and the quality of the linear programming relaxation bound for solving the basic mono-objective variant of the problem. We also propose an epsilon-constraint approach to deal with a bi-objective extension of the problem, in which the number of cutting patterns used must also be minimized. The quality of the models was evaluated through computational experiments on randomly generated instances, yielding promising results.(c) 2022 Published by Elsevier B.V.

Abstract
Cutting and packing problems are hard combinatorial optimization problems that arise in several manufacturing and process industries or in their supply chains. The solution of these problems is not only a scientific challenge but also has a large economic impact, as it contributes to the reduction of one of the major cost factors for many production sectors, namely raw materials, together with a positive environmental impact. The explicit consideration of uncertainty when solving cutting and packing problems with optimization techniques is crucial for a wider adoption of research results by companies. However, current research has paid little attention to the role of uncertainty in these problems. In this paper, we review the existing literature on uncertainty in cutting and packing problems, propose a classification framework, and highlight the many research gaps and opportunities for scientific contributions.