基于决策超图的数学模型用于设计储藏柜

IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Luis Marques, François Clautiaux, Aurélien Froger
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引用次数: 0

摘要

我们研究的问题是设计一个由一组货架组成的橱柜,这些货架上的隔间在打开时会向前滑动。考虑到在给定的时间范围内橱柜中要存放的一组候选物品,问题是设计一组货架和每个货架上的一组隔间,并选择要放入隔间的物品。目标是使所选物品的利润之和最大化。我们将这一问题称为存储柜物理设计(SCPD)问题。SCPD 问题将一个用于设计货架和隔间的两阶段二维背包问题与一组用于选择和分配物品到隔间的时间背包问题结合在一起。我们将 SCPD 问题形式化,将其表述为决策超图中的最大成本流问题,并附加了线性约束。为了缩小该模型的规模,我们打破了对称性,推广了图压缩技术,并利用优势规则来预先计算子问题的解决方案。我们还提出了一系列有效的不等式,以改进模型的线性松弛。我们的经验表明,用我们的改进方法求解弧流模型优于求解 SCPD 问题的紧凑型混合整数线性规划公式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mathematical models based on decision hypergraphs for designing a storage cabinet
We study the problem of designing a cabinet made up of a set of shelves that contain compartments whose contents slide forward on opening. Considering a set of items candidate to be stored in the cabinet over a given time horizon, the problem is to design a set of shelves and a set of compartments on each shelf, and select the items to insert into the compartments. The objective is to maximize the sum of the profits of the selected items. We call our problem the Storage Cabinet Physical Design (SCPD) problem. The SCPD problem combines a two-staged two-dimensional knapsack problem for designing the shelves and compartments with a set of temporal knapsack problems for selecting and assigning items to compartments. We formalize the SCPD problem and formulate it as a maximum cost flow problem in a decision hypergraph with additional linear constraints. To reduce the size of this model, we break symmetries, generalize graph compression techniques and exploit dominance rules for precomputing subproblem solutions. We also present a set of valid inequalities to improve the linear relaxation of the model. We empirically show that solving the arc-flow model with our enhancements outperforms solving a compact mixed integer linear programming formulation of the SCPD problem.
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来源期刊
European Journal of Operational Research
European Journal of Operational Research 管理科学-运筹学与管理科学
CiteScore
11.90
自引率
9.40%
发文量
786
审稿时长
8.2 months
期刊介绍: The European Journal of Operational Research (EJOR) publishes high quality, original papers that contribute to the methodology of operational research (OR) and to the practice of decision making.
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