Abstract
In cutting processes, one of the strategies to reduce raw material waste is to generate leftovers that are large enough to return to stock for future use. The length of these leftovers is important since waste is expected to be minimal when cutting these objects in the future. However, in several situations, future demand is unknown and evaluating the best length for the leftovers is challenging. Furthermore, it may not be economically feasible to manage a stock of leftovers with multiple lengths that may not result in minimal waste when cut. In this paper, we approached the cutting stock problem with the possibility of generating leftovers as a two-stage stochastic program with recourse. We approximated the demand levels for the different items by employing a finite set of scenarios. Also, we modeled different decisions made before and after uncertainties were revealed. We proposed a mathematical model to represent this problem and developed a column generation approach to solve it. We ran computational experi-ments with randomly generated instances, considering a representative set of scenarios with a varying probability distribution. The results validated the efficiency of the proposed approach and allowed us to derive insights on the value of modeling and tackling uncertainty in this problem. Overall, the results showed that the cutting stock problem with usable leftovers benefits from a modeling approach based on sequential decision-making points and from explicitly considering uncertainty in the model and the solution method. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

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 challenging combinatorial optimization problems that have many rel-evant industrial applications and arise whenever a raw material has to be cut into smaller parts while minimizing waste, or products have to be packed, minimizing the empty space. Thus, the optimal solution to these problems has a positive economic and environmental impact. In many practical applications, both the raw material and the cut parts have a rectangular shape, and cut-ting plans are generated for one raw material rectangle (also known as plate) at a time. This is known in the literature as the (two-dimensional) rectangular cutting problem. Many variants of this problem may arise, led by cutting technology constraints, raw-material characteristics, and different planning goals, the most relevant of which are the guillotine cuts. The absence of the guillotine cuts imposition makes the problem harder to solve to optimality.Based on the Floating-Cuts paradigm, a general and flexible mixed-integer programming model for the general rectangular cutting problem is proposed. To the best of our knowledge, it is the first mixed inte-ger linear programming model in the literature for both non-guillotine and guillotine problems. The basic idea of this model is a tree search where branching occurs by successive first-order non-guillotine-type cuts. The exact position of the cuts is not fixed, but instead remains floating until a concrete small rect-angle (also known as item) is assigned to a child node. This model does not include decision variables either for the position coordinates of the items or for the coordinates of the cuts. Under this framework, it was possible to address various different variants of the problem.Extensive computational experiments were run to evaluate the model's performance considering 16 dif-ferent problem variants, and to compare it with the state-of-the-art formulations of each variant. The results confirm the power of this flexible model, as, for some variants, it outperforms the state-of-the-art approaches and, for the other variants, it presents results fairly close to the best approaches. But, even more importantly, this is a new way of looking at these problems which may trigger even better approaches, with the consequent economic and environmental benefits.

Abstract
Many companies face capacity limitations that impair them to satisfy potential demand. In this context, sales/marketing teams have to decide which demand segments the company should prioritize. In business -to-business contexts, it is common that this selection includes customers with and without a contract. On the operations side, the production teams are interested in finding the most efficient usage for the available capacity. However, decision-making approaches to face such a challenge are scarce. In this paper, we propose a scenario-based robust optimization model to support the sales and marketing teams to define the most profitable sales plan in a setting of limited capacity, to serve multiple customers that can be either non -contractual or operate under quantity-flexibility contracts. The proposed model integrates contract design, portfolio selection, and tactical production planning decisions. By employing our model, we are able to quantify how a product's inclusion in a contract relates not only to its own profitability but also to the profitability of the remaining products that might be offered to the customer using the same resources. Regarding the optimal flexibility level to offer to a customer, it is explained by the expected sales volume, the discount rate depending on the flexibility level, and the demand variability expectation. We expect this approach supports industrial companies in defining the mid-term sales plan and deciding on the conditions to offer to contract customers.

Abstract
Tackling uncertainty is becoming increasingly relevant for decision-support across fields due to its critical impact on real-world problems. Uncertainty is often modelled using scenarios, which are combinations of possible outcomes of the uncertain parameters in a problem. Alongside expected value methods, decisions under uncertainty may also be tackled using methods that do not rely on probability distributions and model different decision-maker risk profiles. Scenarios are at the core of these approaches. Therefore, we propose a scenario generation methodology that seizes the structure and concepts of genetic algorithms. This methodology aims to obtain a diverse set of scenarios, evolving a scenario population with a diversity goal. Diversity is here expressed as the difference in the impact that scenarios have on the value of potential solutions to the problem. Moreover, this method does not require a priori knowledge of probability distributions or statistical moments of uncertain parameters, as it is based on their range. We adapt the available code for Biased-Random Key Genetic Algorithms to apply the methodology to a packing problem under demand uncertainty as a proof of concept, also extending its use to a multiobjective setting. We make available these code adaptations to allow the straightforward application of this scenario generation method to other problems. With this, the decision-maker obtains scenarios with a distinct impact on potential solutions, enabling the use of different criteria based on their profile and preferences.