动态规划教学中关于生产库存问题模型求解的改进

Model Solve in Production Inventory on Dynamic Programming Teaching

解决动态规划问题的方法有逆序递推和顺序递推两种。通过实例验证指出,在当前的动态规划应用举例"生产计划问题"最优化模型的求解中,讲解动态规划顺序递推法时,存在不太合理之处。体现在运用动态规划顺序递推法求解过程中涉及到的第k阶段的生产量xk和第k阶段末的库存量vk的取值范围推导不太合理,这能够导致最优解的遗失;同时也会造成学生在学习过程中产生不解和困惑。在对"生产计划问题"的最优化模型进行研究后,按照总的生产成本费用和库存费用之和最小的原则,运用动态规划顺序递推法推导出更为合理的xk和vk的取值范围。

There are two methods to solve dynamic programming problems, backward recursive and forward recursive. When the algorithm of the dynamic programming recursive method was analyzed, example pres- ented shows the common errors about the value range of quantity on the stage k production xk and the stage k storage vk in finding the optimal solution to the implementation of forward recursive equation on dy- namic programming model of production planning problem at present. The result will leads to optimal deci- sion drop out. And also results in students in the learning dynamic programming process generated puzzled and confused. After studying on the dynamic programming model for the production and storage problem, it gives the correct value range of xk and vk based on the principle of the minimization with regard to the total production cost and holding cost.