We propose a novel mixed integer programming (MIP) formulation for a real-world lot-sizing and scheduling problem commonly found in the production of fruit-based beverages, dairy products, among others. The model entails synchronized two-staged production, mandatory temporal cleanings, and sequence-dependent changeovers. In this paper, it appropriately represents industrial production processes of pasteurized juices and fruit flavored juices of different companies. One of the main modeling challenges is to synchronize the two stages that have different temporal cleanings in each stage and are directly connected only when the beverage is being completely transferred from one stage to the other. To the best of our knowledge, there are no studies in the literature that propose MIP formulations for this problem. We also devise fix-and-optimize MIP heuristics to solve realistic large-scale instances from a large worldwide brand company. Computational tests show that they are competitive when compared to the model and the company solutions.

我们提出了一种新颖的混合整数规划（MIP）公式，用于解决基于水果的饮料，乳制品等产品中常见的现实世界中的批量确定和计划问题。该模型需要同步的两阶段生产，强制性临时清洁以及与序列相关的转换。在本文中，它恰当地代表了不同公司的巴氏杀菌果汁和果味果汁的工业生产过程。建模的主要挑战之一是同步两个阶段，每个阶段在每个阶段具有不同的临时清洁，并且仅当饮料从一个阶段完全转移到另一个阶段时才直接连接。据我们所知，文献中没有提出针对此问题提出MIP公式的研究。我们还设计并优化了MIP启发式算法，以解决来自大型全球品牌公司的实际大规模实例。计算测试表明，与模型和公司解决方案相比，它们具有竞争力。