In this paper, we address a variant of a batch scheduling problem with identical parallel machines and non-anticipatory family setup times to minimize the total weighted completion time. We developed an ILS and a GRASP matheuristics to solve the problem using a constructive heuristic and two MIP-based neighborhood searches, considering two batch scheduling mathematical formulations. The problem derives from a ship scheduling problem related to offshore oil & gas logistics, the Pipe Laying Support Vessel Scheduling Problem (PLSVSP). The developed methods overcome the current solution approaches in the PLSVSP literature, according to experiments carried out on a benchmark of 72 instances, with different sizes and characteristics, in terms of computational time and solution quality. New best solutions are provided for all medium and large-sized instances, achieving a reduction of more than 10% in the objective function of the best case.

中文翻译：

---

具有非预期族设置时间的并行机器调度问题的数学：在海上石油和天然气行业中的应用。

在本文中，我们解决了具有相同并行机和非预期系列设置时间的批处理调度问题的变体，以最小化总加权完成时间。我们开发了一个 ILS 和一个 GRASP 数学算法来解决这个问题，使用构造启发式和两个基于 MIP 的邻域搜索，考虑到两个批处理调度数学公式。该问题源自与海上石油和天然气物流相关的船舶调度问题，即管道铺设支持船调度问题 (PLSVSP)。根据在 72 个实例的基准上进行的实验，所开发的方法克服了 PLSVSP 文献中的当前求解方法，这些实例在计算时间和求解质量方面具有不同的大小和特征。