Most solution methods for mixed-integer linear programming (MILP) production scheduling models have been developed for batch processes. In this paper, we employ integer variables, referred to as record keeping variables (RKVs), into discrete-time continuous production scheduling MILP models that facilitate efficient branching and lead to substantial reductions in solution time. We first introduce different types of RKVs and determine which class of RKVs is the most effective. Second, we explore branching priorities and demonstrate that prioritizing branching on RKVs, relative to other binary variables, leads to further computational improvements. Next, we analyze system attributes, such as task and unit utilization, to determine if prioritizing branching on specific RKVs leads to additional computational enhancements. Our computational results show that the proposed reformulations, in combination with implementing branching priorities, lead to significant computational improvements of continuous production scheduling MILP models.

中文翻译：

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使用记录保存变量的连续生产调度 MILP 配方


混合整数线性规划 （MILP） 生产调度模型的大多数求解方法都是为批处理开发的。在本文中，我们将整数变量（称为记录保存变量 （RCV））应用于离散时间连续生产调度 MILP 模型，以促进高效分支并大幅缩短求解时间。我们首先介绍不同类型的 RKV 并确定哪一类 RKV 最有效。其次，我们探讨了分支优先级，并证明相对于其他二进制变量，在 RKV 上优先考虑分支会导致进一步的计算改进。接下来，我们分析系统属性，例如任务和单位利用率，以确定在特定 RKV 上优先分支是否会导致额外的计算增强。我们的计算结果表明，拟议的重新配方与实施分支优先级相结合，导致连续生产调度 MILP 模型的显着计算改进。