存货影响销售率的生产库存系统最优控制策略

摘要

An optimal control model for production-inventory system under stock-dependent selling rate is established in the study. Assuming that inventory is positively related to sales, the model is solved by the Hamiltonian function, application of minimum principle and Laplace transform method. The optimal control function and the corresponding optimal control of the state variables of the optimal trajectory are determined. Moreover, the optimal control strategy for production-inventory system under stock-dependent selling rate is obtained. The research provides theoretical basis for making large-scale production plan of enterprises.%建立了存货影响销售率的生产库存系统最优控制模型。假设存货与销售率的关系是正相关的，研究了存货影响销售率的生产库存系统。通过构造哈密顿函数并应用极小值原理、拉普拉斯变换法对模型进行求解，确定了最优控制函数以及与最优控制相对应的状态变量的最优轨线，得到存货影响销售率的生产库存系统最优控制策略。研究结果为企业规模化生产制定生产计划提供了理论依据。