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中文摘要：
为解决多级、多产品、分散供应链系统生产计划协同问题，提出了一种基于拉格朗日松弛算法的生产计划协同模型。在该模型中，建立每个企业独立的生产计划模型，使用拉格朗日松弛算法，松弛掉企业之间的物流平衡约束，将需要集中决策的供应链生产计划协同问题，分解为企业间分散的独立决策问题；运用次梯度算法对拉格朗日因子进行更新，通过反复迭代的优化过程实现生产计划协同。仿真实验表明，基于拉格朗日松弛算法的供应链协同对复杂供应链系统能够较好地逼近最优解，协同效果和收敛速度优于遗传算法。
英文摘要：
A Lagrange-relaxation algorithm based model was developed to solve the problem of collaborative production planning in distributed supply chain with multi-stage, multi-product characteristics. In this model, the independent production planning model was constructed for each enterprise. Lagrange-relaxation algorithm was used to relax the material flow balance constraints among different enterprises. Thus the integrated decision-making collaboration problem was divided into some independent decision-making issues scattered among enterprises. Subgradient algorithm was used to update the Lagrange multiplier. Through iteration optimization, the collaborative production planning was realized and the nearest optimal solution was achieved. In addition, some simulation experiments were designed to reveal the effects of collaboration model for complicated supply chain. Results showed that the collaboration approach could reach the best solution. And the convergence speed and collaboration effect were better than Genetic Algorithm （GA）.
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