This paper treats a replenishment problem where an order in a single period is to be determined. Demand is assumed to be known for multiple periods. The first periods’ demands are required to be satisfied by the order, satisfying remaining demand is optional. Furthermore, a threshold needs to be satisfied, e.g., a minimum total order volume is given and orders can be placed only if they reach (or exceed) this volume. As a consequence, articles cannot be treated independently and, thus, we have to determine order volumes for all articles integratedly. The replenishment problem with multiple articles and an order threshold is formalized and its computational complexity is determined. We develop mixed-integer programming models and suited optimization approaches and apply them in static and dynamic problem settings. We see that the deterministic problem setting can be solved in reasonable time and that a decision maker can benefit from employing it in a decision support tool in a dynamic environment with uncertainty.

本文讨论了一个补货问题，其中要确定单个期间的订单。假设需求在多个时期内是已知的。订单要求满足第一期的需求，满足剩余需求是可选的。此外，需要满足一个阈值，例如，给出一个最小总订单量，并且只有当它们达到（或超过）这个量时才可以下订单。因此，不能单独处理商品，因此我们必须综合确定所有商品的订单量。将具有多篇文章和订单阈值的补货问题形式化，并确定其计算复杂度。我们开发混合整数编程模型和合适的优化方法，并将它们应用于静态和动态问题设置。