In this paper, we address a two-stage integrated lot-sizing, scheduling and cutting stock problem with sequence-dependent setup times and setup costs. In production stage one, a cutting machine is used to cut large objects into smaller pieces, in which cutting patterns are generated and used to cut the pieces, and should be sequenced in order to obtain a complete cutting plan for the problem. The cut pieces, from production stage one, are used to assemble final products in production stage two, where the final products are scheduled in order to meet the client’s demands. To solve the two-stage integrated problem, we present solution methods based on a price-and-branch approach, in which a column generation procedure is proposed to generate columns and the integer problem is solved by decomposition solution approaches. A computational study is conducted using randomly generated data and an analysis showing the impact of the solution approaches in the two-stage integrated problem is presented. In addition, the performance and benefits of the integrated approach are compared to an empirical simulation of the common practice (sequential approach).

中文翻译：

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集成批量、调度和库存问题的数学模型和求解方法

在本文中，我们解决了一个两阶段集成的批量调整、调度和库存问题，以及与顺序相关的设置时间和设置成本。在生产阶段，使用切割机将大物体切割成更小的碎片，其中生成切割图案并用于切割碎片，并应进行排序，以获得针对问题的完整切割计划。来自第一生产阶段的切割件用于组装第二生产阶段的最终产品，在该阶段安排最终产品以满足客户的需求。为了解决两阶段集成问题，我们提出了基于价格和分支方法的求解方法，其中提出了列生成程序来生成列，并通过分解解法解决整数问题。使用随机生成的数据进行计算研究，并提供了显示解决方法在两阶段集成问题中的影响的分析。此外，将集成方法的性能和优势与常见实践（顺序方法）的经验模拟进行比较。