The Traveling Purchaser Problem (TPP) is a generalization of the TSP that consists in choosing which nodes (markets) to visit to create a tour that allows to buy a set of products at minimum transportation and purchasing cost. The TPP has gained attention due to the computational challenges it poses and the potential applications it can support in today's technology‐driven industry. This paper presents a GRASP‐based methodology for the TPP based on three constructive procedures (route‐first, purchase‐first, and purchase‐and‐route) and two local search operators (insert and remove). The methodology is strengthened with a Path Relinking strategy to improve the GRASP performance by re‐combining a set of elite solutions and with a Filtering strategy to improve the algorithm's efficiency by avoiding local search operations on the least promising solutions. The algorithm is tested with 855 instances of the asymmetric TPP and 190 instances of the symmetric TPP. Computational results prove the benefit of including the Path Relinking and Filtering strategies and suggest that the purchase‐first constructive procedure is the most competitive in terms of objective function value with little extra effort in execution time with respect to the other constructive procedures. Our results outperform published results for the asymmetric TPP in a statistically significant way and show competitive performance for the symmetric TPP.

This article presents a metaheuristic algorithm to solve the pallet-building problem and the loading of these in trucks. This approach is used to solve a real application of a Colombian logistics company. Several practical requirements of goods loading and unloading operations were modeled, such as the boxes’ orientation, weight support limits associated with boxes, pallets and vehicles, and static stability constraints. The optimization algorithm consists of a two-phase approach, the first is responsible for the construction of pallets, and the second considers the optimal location of the pallets into the selected vehicles. Both phases present a search strategy type of GRASP. The proposed methodology was validated through the comparison of the performance of the solutions obtained for deliveries of the logistics company with the solutions obtained using a highly accepted commercial packing tool that uses two different algorithms. The proposed methodology was compared in similar conditions with the previous works that considered the same constraints of the entire problem or at least one of the phases separately. We used the sets of instances published in the literature for each of the previous works. The results allow concluding that the proposed algorithm has a better performance than the most known commercial tool for real cases. The proposed algorithm managed to match most of the test instances and outperformed some previous works that only involve decisions of one of the two problems. As future work, it is proposed to adapt this work to the legal restrictions of the European community.

The material cutting process consists of two NP-hard problems: first, it is necessary to find the optimal cutting pattern to minimize the waste area. Second, it is necessary to find the cutting sequence over the plate to extract the pieces in the shortest possible time. The structure of the cutting path problem can vary according to the technology used in the process. In industries where material can be considered a commodity, the cutting path is decisive due to the need to operate economically and efficiently. These types of minimization demand exact models that use nonconventional formulation techniques in search of computational efficiency and for heuristic processes to be specialized so that a good solution is guaranteed. In this paper, three different approaches were proposed. First, a novel and accurate formulation was presented based on a network flow structure. Second, a reactive GRASP algorithm with solution filtering was designed, using seven operators executed under two randomly selected local search philosophies. Finally, four warm-start variants were designed hybridizing the GRASP algorithm subprocedures with the exact model. The approaches are compared through benchmarking; for this, a set of instances composed of cutting patterns taken from the solution of classical instances of the two-dimensional cutting problem was created and made available. The obtained results show that all three approaches solve the problem successfully. Additionally, the computing time is analyzed, illustrating the pros and cons of each approach. Given the cutting path, including the quality of the pieces is left as a future work proposal.

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