Abstract In this paper, we study a variant of the customer order scheduling problem when sequence-dependent setup times cannot be ignored. The performance measure adopted is the makespan minimization. The existence of sequence-dependent setup times makes this problem to be NP-hard. Furthermore, the solution encoding usually employed for other variants of the customer order scheduling problem does not guarantee finding optimal solutions. For this problem, we present some properties and develop two Mixed Integer Linear Programming (MILP) formulations to analyze the structure of the solutions. Using these properties and models, we propose two matheuristics based on fixing some integer decision variables in the MILP models, denoted as Fixed Variable List Algorithm (FVLA) and Clustering Sequence Algorithm (CSA), respectively. The computational experiments carried out prove the ability of these matheuristics to find high-quality solutions in reasonable CPU time. More specifically, the FVLA matheuristic stands out as the most efficient for the problem.

中文翻译：

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客户订单调度问题，以最小化生产周期与序列相关的设置时间

摘要 在本文中，我们研究了当与序列相关的设置时间不能被忽略时客户订单调度问题的变体。所采用的性能测量是完工时间最小化。依赖于序列的设置时间的存在使这个问题成为 NP-hard。此外，通常用于客户订单调度问题的其他变体的解决方案编码并不能保证找到最佳解决方案。对于这个问题，我们提出了一些属性并开发了两个混合整数线性规划 (MILP) 公式来分析解决方案的结构。使用这些属性和模型，我们提出了两种基于固定 MILP 模型中的一些整数决策变量的数学方法，分别表示为固定变量列表算法（FVLA）和聚类序列算法（CSA）。进行的计算实验证明了这些数学算法在合理的 CPU 时间内找到高质量解决方案的能力。更具体地说，FVLA 数学算法是解决该问题最有效的方法。