This paper investigates a dynamic lot-sizing problem with supplier selection, where the manufacturer develops an aggregate plan to meet product delivery demand with the objective of minimizing the cost. Specifically, a novel supplier selection scenario with varying delivery time quotation is considered, i.e., the manufacturer places raw material replenishment orders with varying delivery time quotation and dynamically selects suppliers, and the suppliers guarantee delivery within the quoted delivery lead time. In the dynamic lot-sizing problem with supplier selection, a joint decision on the production plan, replenishment order, and supplier selection needs to be made. To tackle this complex problem, a modified Variable Neighborhood Search algorithm with nested two parallel neighborhoods (PN-VNS) is first developed for the decision on the production plan and replenishment order. Then, the decision on supplier selection needs to be made for the given replenishment order, and a pre-pruning optimization rule is proposed to obtain the optimal supplier scheme. Computational experiments are conducted to evaluate the performance of the proposed algorithm, and the experimental results demonstrate that our algorithm performs better both in terms of solution quality and running time.

本文研究了供应商选择的动态批量问题，其中制造商制定总体计划来满足产品交付需求，以最大限度地降低成本。具体来说，考虑了一种新颖的不同交货时间报价的供应商选择场景，即制造商以不同交货时间报价下原材料补货订单并动态选择供应商，供应商保证在报价的交货提前期内交货。在涉及供应商选择的动态批量问题中，需要对生产计划、补货订单和供应商选择做出联合决策。为了解决这个复杂的问题，首先开发了一种改进的具有嵌套两个并行邻域的可变邻域搜索算法（PN-VNS），用于决策生产计划和补货订单。然后，需要针对给定的补货订单做出供应商选择决策，并提出预剪枝优化规则以获得最优供应商方案。进行了计算实验来评估所提出算法的性能，实验结果表明我们的算法在解质量和运行时间方面都表现更好。