Abstract There are several mathematical models proposed for the facility location and production planning problem in the literature. However, some of these models disregard what products each customer has ordered and neglect critical production-related constraints and setup decisions while some others do not well define the connection cost between customers and facilities. In this study, we propose two mathematical models to overcome the disadvantages aforementioned, along with their reformulations by item decomposition to improve lower bounds. We demonstrate that the pricing subproblems of the item decomposition are related to uncapacitated lot-sizing problems with the Wagner-Whitin property. This property is employed to enhance the performance of column generation for the item decomposition. Our computational results show that this item decomposition method can improve lower bounds over other classical lower bounding techniques, such as linear programming relaxation and model reformulation. Additionally, we implement the proposed item decomposition method to other benchmark problems in the literature and observe that our proposed method can improve the benchmark solutions with a statistical significance.

中文翻译：

---

工厂位置和生产计划问题的 Dantzig-Wolfe 分解

摘要 文献中针对设施选址和生产计划问题提出了几种数学模型。然而，其中一些模型忽略了每个客户订购的产品，并忽略了与生产相关的关键约束和设置决策，而其他一些模型没有很好地定义客户和设施之间的连接成本。在这项研究中，我们提出了两种数学模型来克服上述缺点，并通过项目分解重新制定它们以提高下界。我们证明了项目分解的定价子问题与 Wagner-Whitin 属性的无容量批量大小问题有关。此属性用于增强项目分解的列生成性能。我们的计算结果表明，与其他经典下界技术（例如线性规划松弛和模型重构）相比，该项目分解方法可以提高下界。此外，我们将提出的项目分解方法应用于文献中的其他基准问题，并观察到我们提出的方法可以改进具有统计显着性的基准解决方案。