This paper investigates the multi-level warehouse layout problem with indeterminate factors, in which the monthly demands and horizontal transportation distances are described by uncertain variables. We first consider the distribution function of the total cost for transportation. Second, two uncertain models, namely, the chance-constrained programming model and the chance-maximum programming model, are developed to lay out the multi-level warehouse under uncertainty. Some properties of the models are discussed to solve the models. The properties point out that the optimal solution to the chance-constrained programming model is equivalent to a corresponding deterministic model. Additionally, we also discuss the relation between the chance-constrained programming model and the chance-maximum programming model, which leads to an effective approach to search for the optimal solution to the chance-maximum programming model. Finally, a numerical experiment is illustrated to show the ideas of the proposed models.

中文翻译：

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信息不确定的多层次仓库布局问题：不确定性理论方法

本文研究了具有不确定因素的多层次仓库布局问题，其中月需求和水平运输距离由不确定变量描述。我们首先考虑运输总成本的分布函数。其次，开发了机会约束规划模型和机会最大规划模型两种不确定模型，对不确定性下的多级仓库进行布局。讨论了模型的一些属性来求解模型。性质指出机会约束规划模型的最优解等价于相应的确定性模型。此外，我们还讨论了机会约束规划模型和机会最大规划模型之间的关系，这导致了一种有效的方法来搜索机会最大规划模型的最佳解决方案。最后，通过数值实验说明了所提出模型的思想。