基于几类订货费用的连续盘点随机库存优化问题

In practice, the ordering cost is often a general function of order quantity. For example, multiple setup costs, incremental discount and all-unit discount are the ordering costs usually used in inventory management. So far, these ordering costs are considered only in the period review inventory models but the optimal policies are not completely solved; On the other hand, they have not been considered in the continuous review inventory models with stochastic process demand yet. Motivated by the wide applications and insufficient research, this project studies these ordering costs by modeling customers’ demand respectively as jump process (compound Poisson process) and diffusion process (including Brownian motion, Geometric Brownian motion etc.) to consider these several ordering costs, establishes the corresponding inventory models, and analyzes the optimal policies for these inventory systems. Further, this project also studies whether and why the jump process demand and diffusion process demand lead to different optimal ordering policies. In addition, we consider the inventory models with demand described by jump process plus diffusion process. This project plans to establish an approach to solve the continuous review stochastic inventory models with these several ordering costs, developing stochastic inventory theory, and reducing costs in inventory management.

在现实情况中，订货费用往往是订货量的一般函数，例如多固定费用、增量折扣和全数量折扣等都是实际库存管理中常用的订货费用。到目前为止，这些订货费用仅在周期盘点的库存模型中被研究，但其最优策略尚未被完全刻画。同时这些订货费用还没有在顾客需求为随机过程的连续盘点库存模型中被研究过。基于此，本项目采用跳过程（复合泊松过程）和扩散过程（包括布朗运动、几何布朗运动等）两类随机过程分别模拟库存系统的顾客需求，考虑这几类订货费用函数，并建立相应的库存优化模型，分析库存模型的最优订货策略。进一步，项目研究在相同订货费用函数下，跳过程需求与扩散过程需求是否导致最优订货策略结构的不同，并分析其原因。另外，项目研究两个过程相结合的需求库存模型。本项目拟建立一套随机优化方法来解决基于几类订货费用的连续盘点随机库存模型，完善随机库存优化理论，并将其应用于减少企业库存管理费用。

在现实中，订货费用往往是订货量的一般函数，例如多固定费用、增量折扣费用和全数量折扣费用等都是实际库存管理中常见的订货费用。本项目研究之前，这些订货费用费用仅在周期盘点的库存模型中被研究，并且其最优策略也未被完全刻画出。同时，这些订货费用也还没有在顾客需求为随机过程的连续盘点库存模型中被研究过。基于此，本项目采用布朗运动、一般扩散过程以及跳过程分别模拟库存系统的顾客需求，考虑这几类订货费用函数，建立了相应的库存优化模型，完全刻画出了库存模型的最优订货策略。进一步，项目研究表明在相同的订货费用函数下，扩散过程和跳过程会导致最优订货策略结构的不同。另外，本项目也建立了一套最优下界方法来解决基于几类订货费用函数的连续盘点随机库存模型，完善了随机库存优化理论，并期望对减少企业库存管理费用提供帮助。总之，受本项目资助，申请人已发表4篇高水平论文，其中两篇发表在相关领域的国际顶尖级杂志。