Abstract
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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
The Vehicle Routing Problem with Divisible Deliveries and Pickups (VRPDDP) is under-explored in literature, yet it has a wide application in practice in a reverse logistics context, where the collection returnable items must also be ensured along with the traditional delivery of products to customers. problem considers that each customer has both delivery and pickup demands and may be visited twice in the same or different routes (i.e., splitting customers' visits). In several reverse logistics problems, capacity restrictions are required to either allow the movement of the driver inside the vehicle to arrange the loads or to avoid cross-contamination between delivery and pickup loads. In this work, explore the economic and the environmental impacts of the VRPDDP, with and without restrictions the free capacity, and compare it with the traditional Vehicle Routing Problem with Simultaneous Deliveries and Pickups (VRPSDP), on savings achieved by splitting customers visits. An exact method, solved through Gurobi, and an ALNS metaheuristic are coded in Python and used to test well-known and newly generated instances. A multi-objective approach based on the augmented e-constraint method is applied to obtain and compare solutions minimizing costs and CO2 emissions. The results demonstrate that splitting customer visits reduces the CO2 emissions for load-constrained distribution problems. Moreover, savings percentage of the VRPDDP when compared to the VRPSDP is higher for instances with a random network than when a clustered network of customers is considered.

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Abstract
Cutting and packing problems have been widely studied in the last decades, mainly due to the variety of industrial applications where the problems emerge. This paper presents an overview of the solution approaches that have been proposed for solving two-dimensional rectangular cutting and packing problems. The main emphasis of this work is on two distinct problems that belong to the cutting and packing problem family. The first problem aims to place onto an object the maximum-profit subset of items, that is, output maximization, while the second one aims to place all the items using as few identical objects as possible, that is, input minimization. The objective of this paper is not to be exhaustive but to provide a solid grasp on two-dimensional rectangular cutting and packing problems by describing their most important solution approaches.

Abstract
We approached the two-dimensional rectangular strip packing problem (2D-SPP), where the main goal is to pack a given number of rectangles without any overlap to minimize the height of the strip. Real-life constraints must be considered when developing 2D-SPP algorithms to deliver solutions that will improve the cutting processes. In the 2D-SPP literature, a gap related to studies approaching constraints in real-life scenarios was identified. Therefore, the impact of real-life constraints found in the plasma cutting process in sheet metal waste was analyzed. A mathematical model from the literature was modified to obtain packing arrangements with plasma cutting constraints. The combination of size and number of rectangles, as well as strip width, was the main factor that affected the packing arrangement, limiting the allocation of rectangles and generating empty spaces. In summary, considering the sheet metal waste context, instances with smaller widths should be avoided in practical operations for high minimum distance constraint values, returning the worst packing arrangements. For low minimum distance constraint values, smaller width instances can be used in practical operations, as the packing arrangement is acceptable. Finally, this article can reduce material waste and enhance the cutting process in the sheet metal industry, by showing packing characteristics which lead to higher amounts of raw material waste.