The paper studies a one-dimensional multiple stock size cutting stock problem (1D-MSSCSP) with multiple suppliers selection procurement problem (MSSPP) from the perspective of supply chains. According to the requirement of global optimization for enterprise business, a coordination optimization model of procurement with multiple suppliers selection and one-dimensional cutting stock with multiple stock lengths is formulated. The model's objective is to minimize total costs of the stock, ordering and setup. Lagrangian relaxation approach is employed to relaxing a certain type of constraint. A hybrid heuristic method called Lagrangian-based cutting and procurement heuristic based on the methods of column generation, branch-and-bound and subgradient, is developed. It consists of two sub-algorithms, one is for 1D-MSSCSP, the other is for MSSPP. Finally, more than 180 instances randomly generated have been solved by using the proposed method. The calculation results demonstrate the validity of the proposed model and the corresponding solving method.%研究多供应商选择的一维多母材下料问题.基于企业经营过程全局最优化要求,建立了多供应商采购与一维多母材下料协调优化模型,最小化母材购买成本,订购成本及作业准备成本.用拉格朗日松弛技术对有关约束进行松弛和模型分解,设计基于列生成法、分枝定界和次梯度算法的混合启发式算法.该算法由两部分组成,分别用于求解一维多母材下料子问题和多供应商采购子问题.最后,通过随机产生的180个算例,验证模型合理性与算法的有效性.
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