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
Trade promotions are complex marketing agreements between a retailer and a manufacturer aiming to drive up sales. The retailer proposes numerous sales promotions that the manufacturer partially supports through discounts and deductions. In the Portuguese consumer packaged goods (CPG) sector, the proportion of price-promoted sales to regular-priced sales has increased significantly, making proper promotional planning crucial in ensuring manufacturer margins. In this context, a decision support system was developed to aid in the promotional planning process of two key product categories of a Portuguese CPG manufacturer. This system allows the manufacturer’s commercial team to plan and simulate promotional scenarios to better evaluate a proposed trade promotion and negotiate its terms. The simulation is powered by multiple gradient boosting machine models that estimate sales for a given promotion based solely on the scarce data available to the manufacturer. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Abstract
When dealing with cutting problems, the generation of usable leftovers proved to be a good strategy for decreasing material waste. Focusing on practical applications, the main challenge in the implementation of this strategy is planning the cutting process to produce leftovers with a high probability of future use without complete information about the demand for any ordered items. We addressed the two-dimensional cutting stock with usable leftovers and uncertainty in demand, a complex and relevant problem recurring in companies due to the unpredictable occurrence of customer orders. To deal with this problem, a two-stage formulation that approximates the uncertain demand by a finite set of possible scenarios was proposed. Also, we proposed a matheuristic to support decision-makers by providing good-quality solutions in reduced time. The results obtained from the computational experiments using instances from the literature allowed us to verify the matheuristic performance, demonstrating that it can be an efficient tool if applied to real-life situations.

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.

Abstract
This paper presents a C++ application programming interface for a co-evolutionary algorithm for solution and scenario generation in stochastic problems. Based on a two-space biased random-key genetic algorithm, it involves two types of populations that are mutually impacted by the fitness calculations. In the solution population, high-quality solutions evolve, representing first-stage decisions evaluated by their performance in the face of the scenario population. The scenario population ultimately generates a diverse set of scenarios regarding their impact on the solutions. This application allows the straightforward implementation of this algorithm, where the user needs only to define the problem-dependent decoding procedure and may adjust the risk profile of the decision-maker. This paper presents the co-evolutionary algorithm and structures the interface. We also present some experiments that validate the impact of relevant features of the application.