Search Results (5)

Background: The Irregular Strip Packing Problem (ISPP) involves packing a set of irregularly shaped items within a strip while minimizing its length. Methods: This study introduces the Normalized Direct Trigonometry Model (NDTM), an innovative enhancement of the Direct Trigonometry Model (DTM). The NDTM incorporates a distance function that supports the integration of the separation constraint, which mandates a minimum separation distance between items. Additionally, the paper proposes a new set of constraints based on the bounding boxes of the pieces aimed at improving the non-overlapping condition. Results: Comparative computational experiments were performed using a comprehensive set of 90 instances. Results show that the NDTM finds more feasible and optimal solutions than the DTM. While the NDTM allows for the implementation of the separation constraint, the number of feasible and optimal solutions tends to decrease as more separation among the items is considered, despite not increasing the number of variables or constraints. Conclusions: The NDTM outperforms the DTM. Moreover, the results indicate that the new set of non-overlapping constraints facilitates the exploration of feasible solutions at the expense of optimality in some cases. Full article

The two-dimensional strip-packing problem (2D-SPP) emerges as a notable variant of the cutting and packing (C&P) problem, aiming to optimize the arrangement of small rectangular items within unique strips with a fixed width and infinite height to minimize the usage of height. Despite extensive academic exploration, applying 2D-SPP solutions in industrial settings remains challenging. Two significant issues, often overlooked in academia yet frequently encountered in industrial contexts, are the uncertain demand for items, exacerbated by the bullwhip effect, and the need for diverse types of strips to cater to varying customer needs. Our paper addresses this academia–industry gap by proposing a robust optimization model for the uncertain 2D-SPP with variable-sized bins, aiming to manage the demand fluctuations within a box uncertainty set framework. Additionally, we employ the contiguous one-dimensional relaxation technique in conjunction with column generation to tighten the lower bound of the problem, thereby augmenting solution accuracy. Furthermore, we leverage the Karush–Kuhn–Tucker (KKT) condition to transform the model into a more tractable form, subsequently leading to an exact solution. Based on datasets from a real-life plastic-cutting company, comprehensive experiments validate the effectiveness and efficiency of our proposed relaxation method and algorithm, showcasing the potential for an improved industrial application of 2D-SPP solutions. Full article

Crowdsourcing offers on-demand access to large numbers of human workers to implement new forms of human–computer collaborative functionalities that can be seamlessly integrated into advanced software and algorithms. However, crowdsourcing tasks are primarily undertaken by urban rather than rural workers. To enable the development of skilled rural employment, this research aims to assess rural crowdsourcing workers’ spatial reasoning and creative abilities and their abilities to solve irregular strip packing problems associated with the manufacture of sheet materials. The study conducted experiments and data collection with 140 rural Business Processing Outsourcing (BPO) workers located in six states of India. The statistical analyses of the data collected from seven rural BPO firms (140 rural workers) reveal that rural workers can achieve a 2D packing efficiency that is up to 8% higher than that of commercial algorithm outcomes. The results suggest that rural crowdsourcing can lead to effective job creation, skill development, and, for a modest cost, it can support industries that employ CAD/CAM systems to generate geometric data for common manufacturing processes. Full article

Rural preferential loans usually take the form of portfolio credits. From the perspective of public interest, the total delay time for obtaining loans is expected to be minimized. To use rural portfolio credits effectively, the two-dimensional strip packing grouping delay problem (2SPGDP) is improved to optimize the rural portfolio credit granting system. First, 2SPGDP is established by adding grouping constraints and the latest start time constraints to the two-dimensional strip packing problem, and the total delay is taken as the optimization objective. Second, based on the depth search reverse spanning tree (DSRST) and the insert spare space (ISS) method, the branch-and-bound reverse order insert algorithm (BB-RIA) is designed. Finally, the lag pruning operator (LPO) is designed to reduce lag. The improved model (2SPGDP) and BB-RIA-LPO algorithm are used to solve several classical two-dimensional strip packing problems and a specific rural portfolio credit case. Compared with the Bottom-Left and Branch and Bound Algorithm, our model and algorithm improve the success rate by 25% and reduce the total delay by 6%. The case of rural portfolio credit illustrates the operability and effectiveness of this method. Full article

This research addresses the two-dimensional strip packing problem to minimize the total strip height used, avoiding overlapping and placing objects outside the strip limits. This is an NP-hard optimization problem. We propose a greedy randomized adaptive search procedure (GRASP), incorporating flags as a new approach for this problem. These flags indicate available space after accommodating an object; they hold the available width and height for the following objects. We also propose three waste functions as surrogate objective functions for the GRASP candidate list and use and enhanced selection for the restricted candidate list, limiting the object options to better elements. Finally, we use overlapping functions to ensure that the object fits in the flag because there are some cases where a flag’s width can be wrong due to new object placement. The tests showed that our proposal outperforms the most recent state-of-the-art metaheuristic. Additionally, we make comparisons against two exact algorithms and another metaheuristic. Full article