两种销售渠道间的库存分配问题

Inventory Allocation between Two Sales Channels

库存系统同时为两个下游节点供货。两个节点分别对应于两种销售渠道。其中,一个节点处需求是依赖于即时库存量的线性函数,通过求解常微分方程得到该节点的即时库存量变化规律;另一节点处需求是与即时库存量无关的随机变量。在可用库存量为给定值的条件下,基于一阶最优性条件给出最优库存分配策略,并利用目标函数的凹性及其导数的单调性等性质分析第一个节点处需求与库存量之间的依赖关系对最优库存分配策略的影响,给出两者间的单调依赖关系。在随机生成的50组参数下,数值实验显示忽略需求与库存量之间的依赖关系会造成不可忽视的利润损失。

An inventory system supplies two downstream nodes,which correspond to two sales channels.In one of the nodes,demand is deterministic with a stock-dependent arriving rate,while the other node serves stochastic demand following a given random distribution.Under the condition that the available stock for allocation is given,we solve the optimal inventory allocation problem between the two nodes,based on the first-order optimality condition.Furthermore,we utilize properties,such as the concavity of the objective function and the monotonicity of its derivative,to characterize how the dependency between inventory and demand affects the optimal inventory allocation decision.Under the randomly generated 50 groups of parameters,a numerical experiment shows that ignoring the inventory-demand dependency leads to considerable loss of profit.