需求依赖库存的生产库存系统的最优控制

针对现实生活中存在的库存刺激需求的现象,建立了生产库存系统的最优控制模型.模型中生产率和价格为控制变量,库存为状态变量,并且生产率是有界的,需求率同时依赖于库存和价格.运用最大值原理对模型进行求解,根据模型参数的不同取值,获得了三种可能的解,并对其进行了详细分析.最后将模型应用于具体算例,得到了系统状态的具体变化过程,通过与需求不依赖于库存的情形相比较,得到了需求依赖于库存所产生的影响.

Optimal control of production inventory systems with inventory-level-dependent demand

Considering the phenomenon of inventory stimulating demand in real life, this article introduces an optimal control model of production inventory systems. In this model, the production rate and price level are control variables, the production rate is bounded, the inventory level is state variables, and the demand rate depends on the inventory level and price level. Three possible solutions are achieved according to different values of model parameters using the maximum principle and are analyzed in detail. By applying the model to a numerical example, a concrete transformation process of the system state is presented. In comparison with the case that demand does not depend on inventory, the impact of demand depending on inventory comes to light.