This article addresses a real-world tactical production planning problem in which a series of real-world constraints need to be considered, such as no backorder, products with multilevel bills of material (BOMs), and lot streaming production. Under the premise of no backorder, the objective of this plan is to make the workload as balanced as possible throughout the planning horizon. An integer quadratic programming model is first proposed to formulate this problem. Then, based on the analysis of the optimal solution for a common BOM structure, this problem is reformulated to a simplified problem where only one item in BOM needs to be considered. Some optimality properties are further derived to help solve this problem. An enhanced variable neighborhood search algorithm is developed to solve this problem, and a lower bound is put forward to measure the performance of the algorithm. Experimental results show that this algorithm can obtain high-quality solutions in a short time.

中文翻译：

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通过批次流和多级 BOM 实现生产计划的工作负载平衡


本文解决了现实世界的战术生产计划问题，其中需要考虑一系列现实世界的约束，例如无延期交货、具有多级物料清单 (BOM) 的产品以及批量流式生产。在不缺货的前提下，该计划的目标是使整个计划范围内的工作量尽可能平衡。首先提出了整数二次规划模型来解决这个问题。然后，基于对常见BOM结构的最优解的分析，该问题被重新表述为仅需要考虑BOM中的一项的简化问题。进一步导出一些最优性属性来帮助解决这个问题。为了解决这个问题，提出了一种增强的变量邻域搜索算法，并提出了一个下界来衡量算法的性能。实验结果表明，该算法能够在短时间内获得高质量的解。