A B S T R A C T Shelf space is one of the scarcest resources, and its effective management to maximize profits has become essential to gain a competitive advantage for retailers. We consider the shelf space allocation...
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A B S T R A C T Shelf space is one of the scarcest resources, and its effective management to maximize profits has become essential to gain a competitive advantage for retailers. We consider the shelf space allocation problem with additional features (e.g., integer facings, rectangular arrangement restrictions) motivated by litera-ture and our interactions with a local bookstore. We determine optimal number of facings of all products in two aspects (width and height of a rectangular arrangement space for each product), and allocate them as contiguous rectangles to maximize profit. We first develop a mixed-integer linear mathematical programming model (MIP) for our problem and propose a solution method based on logic-based Ben-ders decomposition (LBBD). Next, we construct an exact 2-stage algorithm (IP1/IP2), inspired by LBBD, which can handle larger and real-world size instances. To compare performances of our methods, we generate 100 test instances inspired by real-world applications and benchmarks from the literature. We observe that IP1/IP2 finds optimal solutions for real-world instances efficiently and can increase the local bookstore's profit up to 16.56%. IP1/IP2 can provide optimal solutions for instances with 100 products in minutes and optimally solve up to 250 products (assigned to 8 rows x 160 columns) within a time limit of 1800 s. This exact 2-stage IP1/IP2 solution approach can be effective in solving similar problems such as display problem of webpage design, allocation of product families in grocery stores, and flyer advertising. (c) 2021 Elsevier B.V. All rights reserved.
The adoption of hybrid GPU-CPU nodes in traditional supercomputing platforms such as the Cray-XK6 opens acceleration opportunities for electronic structure calculations in materials science and chemistry applications,...
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ISBN:
(纸本)9780769549569;9781467362184
The adoption of hybrid GPU-CPU nodes in traditional supercomputing platforms such as the Cray-XK6 opens acceleration opportunities for electronic structure calculations in materials science and chemistry applications, where medium-sized generalized eigenvalue problems must be solved many times. These eigenvalue problems are too small to effectively solve on distributed systems, but can benefit from the massive compute performance concentrated on a single node, hybrid GPU-CPU system. However, hybrid systems call for the development of new algorithms that efficiently exploit heterogeneity and massive parallelism of not just GPUs, but of multi/many-core CPUs as well. Addressing these demands, we developed a novel algorithm featuring innovative: Fine grained memory aware tasks, Hybrid execution/scheduling, and Increased computational intensity. The resulting eigensolvers are state-of-the-art in HPC, significantly outperforming existing libraries. We describe the algorithm and analyze its performance impact on applications of interest when different fractions of eigenvectors are needed by the host electronic structure code.
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