利用拉格朗日松弛算法协调多厂供应链生产计划

为了解决多厂供应链生产计划的协调问题，提出了一种基于拉格朗日松弛算法的内部价格协调优化策略。该策略通过松弛工厂之间的物料耦合约束，将整个供应链的生产计划问题分解为多个单厂的生产计划问题。每个工厂只需利用本地信息制定各自的生产计划。为了获取问题的可行解，又提出了一种前溯式可行化方法，通过协调中心对产品内部价格（拉格朗日算子）的迭代更新，实现整个供应链生产计划的协调优化。仿真实验表明，该策略能够较好地协调多厂供应链计划，结果明显优于已有的协调方法。

Coordination method for multi-plants supply chain production planning based on Lagrange relaxation algorithm

To solve coordination problem of multi-plants supply chain production planning, a coordination and optimization strategy of internal price based on Lagrange relaxation algorithm was presented. By relaxing the material flow balance constraints among plants with the internal price, i.e. Lagrange multipliers, the whole supply chain production planning problem was decomposed into multiple single-plant production planning sub-problems, each of which could make its own production plan through local information. In order to obtain the feasible solution, a distributed retrospective heuristics algorithm was introduced. During the coordination process, through iterative update of the internal price for each kind of products provided by the coordination center, the supply chain could be coordinated and the nearest optimal solution could be achieved. The simulation experiments showed that the method could better solve the multi-plants supply chain production planning problem and was superior to the existing coordination methods.