Abstract In today's centralized globalized economy, large manufacturing firms operate more than one production center. Therefore, the multifactory production scheduling environment, so-called the distributed scheduling problem, is gaining more and more attention from the authors. In this context, which factory will manufacture which product is an important decision making process. The distributed permutation flowshop scheduling problem (DPFSP) provided with real life applications has attracted attention of the researchers for nearly one decade as one of the special cases of the distributed scheduling problem. In the current literature, approximation methods have been intensely used for solving the DPFSP and only one paper containing the exact solution methods has been published to solve this problem. In this paper, the best mathematical formulations available in the current literature has been further improved and traditional and hybrid Benders decomposition algorithms are presented through the proposed new mathematical model. The developed new model is a position based model intended for restricting the domains of decision variables and assigning jobs to sequential positions in the related decision variables. The proposed hybrid Benders decomposition algorithm consists of the hybridization of NEH2_en local search algorithm, a mathematical model to find the upper bound for the number of positions used in the related decision variables, the LS3 algorithm, with the Benders decomposition algorithms. The new and best exact methods available in the literature are compared with each other by using the benchmark data sets and the experimental results showed that the new exact methods developed in this paper are superior to the existing exact methods in all aspects. In this paper, 18 new best solutions are founded for the DPFSP.

中文翻译：

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一种求解分布式置换流水车间调度问题的有效Benders分解算法

摘要 在当今中心化的全球化经济中，大型制造企业经营着不止一个生产中心。因此，多工厂生产调度环境，即所谓的分布式调度问题，越来越受到作者的关注。在这种情况下，哪个工厂将生产哪种产品是一个重要的决策过程。提供现实生活应用的分布式置换流水车间调度问题（DPFSP）作为分布式调度问题的特例之一，近十年来引起了研究人员的关注。在当前的文献中，近似方法已被广泛用于解决 DPFSP，并且仅发表了一篇包含精确解法的论文来解决这个问题。在本文中，当前文献中可用的最佳数学公式得到了进一步改进，并通过提出的新数学模型呈现了传统和混合 Benders 分解算法。开发的新模型是一种基于职位的模型，旨在限制决策变量的域并将工作分配到相关决策变量中的连续职位。所提出的混合 Benders 分解算法由 NEH2_en 局部搜索算法、一种用于找到相关决策变量中使用的位置数的上限的数学模型、LS3 算法与 Benders 分解算法的混合组成。通过使用基准数据集将文献中可用的新的和最佳的精确方法相互比较，实验结果表明，本文开发的新精确方法在各个方面都优于现有的精确方法。在本文中，为 DPFSP 建立了 18 个新的最佳解决方案。