Abstract This study addresses a planning problem for plastics injection systems, where final products are assembled of compatible plastic pieces. Additionally, the production of pieces requires the use of dedicated molds that are installed on compatible injection machines (leading to long setup times). Then, our Manufacturing Planning Problem determines the lot-size of each product in terms of the number of cycles for each piece–mold–machine combination and the scheduling of molds for each injection machine in a single planning period to maximize the total profit. We consider constraints for machines’ available time and avoid mold overlapping on different machines. Moreover, we define a mixed-integer linear program for our problem, and we obtain high-quality solutions for medium-size instances using a commercial solver in minutes. Still, the convergence to optimal solutions for large instances is slower. In response, we propose a two-stage sequential approach that takes advantage of the mathematical formulation to obtain better solutions for large instances in short computational times.

中文翻译：

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在塑料注射系统的背景下，用于批量大小决策的两阶段顺序方法

摘要 本研究解决了塑料注射系统的规划问题，其中最终产品由兼容的塑料件组装而成。此外，零件的生产需要使用安装在兼容注塑机上的专用模具（导致设置时间长）。然后，我们的制造计划问题根据每个零件-模具-机器组合的周期数和每个注塑机在单个计划期内的模具调度来确定每个产品的批量，以最大化总利润。我们考虑机器可用时间的限制，并避免模具在不同机器上重叠。此外，我们为我们的问题定义了一个混合整数线性程序，并且我们在几分钟内使用商业求解器为中等大小的实例获得了高质量的解决方案。仍然，大型实例的最优解收敛速度较慢。作为回应，我们提出了一种两阶段顺序方法，该方法利用数学公式在较短的计算时间内为大型实例获得更好的解决方案。