需求依赖库存水平的随机库存模型

Stochastic Inventory Model with Supply and Demand Based on Inventory Level

对供货方式和库存周期进行优化可以进一步提高库存效益.传统库存模型视供给、需求、库存水平相互独立,放宽这一假定,采用微分方程描述供给、需求与库存量之间的关系,并考虑了需求的随机波动.将库存成本表示为订货费、保管费、残余库存损失费和缺货损失费的叠加,根据需求的波动范围,定义了平衡、缺货、残余三种库存状态,结合一次补齐和整周期连续补货模型,利用库存成本期望提出了基于补货周期的随机库存模型.以库存系统效益最大化为目标函数,以库存容量为约束条件建立了库存优化模型,基于偏导数方程,利用一元Taylor展开式对方程进行简化,并设计了迭代求解算法.算例分析结果表明,模型可以有效地降低库存水平.

The optimization of supply mode and inventory cycle can further improve inventory efficiency. Traditional inventory models assume the mutually independent relationship among supply rate, demand rate and stock-level. Relaxing the assumption, functional relationship is described with the differentialequation in consideration of random fluctuations in demand. The inventory cost is expressed as the superposition of order fee, storage fee, residual inventory loss fee and shortage loss fee. According to the fluctuation range of demand, the three inventory states of balance, shortage and residual are defined.A stochastic inventory model based on replenishment cycle is proposed by using inventory cost expectation in combination with a one-time replenishment model and a whole-cycle continuous replenishment model. Taking the benefit maximization of the inventory system as the objective function and the inventory capacity as the constraint condition, the inventory optimization model is established. Based on the partial derivative equation, the equation is simplified by using the unary Taylor expansion, and an iterative solution algorithm is designed.Example analysis results indicate that the stochastic inventory model can effectively reduce the inventory level.