Abstract This work considers the optimal production planning and scheduling problem in beer production facilities. The underlying optimization problem is characterized by significant complexity, including multiple production stages, several processing units, shared resources, tight design and operating constraints and intermediate and final products. Breweries are mainly differentiated to the rest of the beverage industries in terms of long lead times required for the fermentation/maturation process of beer. Therefore, synchronizing the production stages is an extremely challenging task, while the long time horizon leads to larger and more difficult optimization problems. In this work we present a new MILP model, using a mixed discrete-continuous time representation and the immediate precedence framework in order to minimize total production costs. A number of test cases are used to illustrate the superiority of the proposed model in terms of computational efficiency and solution quality compared with approaches developed in other research contributions. The proposed model provides consistently better solutions and improvements of up to 50% are reported. In order to address large-scale problem instances and satisfy the computation limitations imposed by the industry, a novel MILP-based solution strategy is developed, that consists of a constructive and an improvement step. As a result, near-optimal solutions for extremely large cases consisting of up to 30 fermentation tanks, 5 filling lines and 40 products are generated in less than two hours. Finally, the proposed method is successfully applied to a real-life case study provided by a Greek brewery and near-optimal schedules are generated in relatively short CPU times.

中文翻译：

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啤酒厂的最佳生产计划和调度

摘要 这项工作考虑了啤酒生产设施中的最优生产计划和调度问题。底层优化问题的特点是非常复杂，包括多个生产阶段、多个处理单元、共享资源、严格的设计和操作约束以及中间产品和最终产品。啤酒厂与其他饮料行业的主要区别在于啤酒发酵/成熟过程所需的较长交货时间。因此，同步生产阶段是一项极具挑战性的任务，而较长的时间范围会导致更大和更困难的优化问题。在这项工作中，我们提出了一个新的 MILP 模型，使用混合离散连续时间表示和直接优先框架，以最小化总生产成本。与其他研究贡献中开发的方法相比，许多测试用例用于说明所提出的模型在计算效率和解决方案质量方面的优越性。提议的模型始终提供更好的解决方案，并且报告了高达 50% 的改进。为了解决大规模问题实例并满足行业强加的计算限制，开发了一种新的基于 MILP 的解决方案策略，包括建设性和改进步骤。因此，在不到两小时的时间内为由多达 30 个发酵罐、5 条灌装线和 40 种产品组成的超大型案例生成了近乎最佳的解决方案。最后，