随机供应中断和退货环境下库存问题的建模与控制

摘要

Uncertainties in supply disruptions and returns make it extremely hard to control a firm0s inventory. However, the traditional approach is found quite difficult to develop a model due to many stochastic factors in the system, therefore supply disruptions and returns are dealt with separately. In order to analyze their effects on the firm0s inventory com-prehensively, under the condition that the inventory level process is expressed as a Brownian motion (BM), an expected total discounted cost model is established by utilizing continuous-time Markov chain, renewal process and martingale theorems. Subsequently, a cross-entropy method is designed to obtain the optimal inventory policy. Numerical results are provided to illustrate the influences of disruptions, net demands and system parameters on the optimal control policy and the expected discounted cost.%供应中断和退货的不确定性，导致企业库存控制异常困难。然而，由于系统存在多个随机因素，采用传统方法很难构建模型，所以，以往均将供应中断和退货分开考虑。为综合分析它们对库存的影响，本文在采用布朗运动描述库存水平动态变化过程条件下，利用连续时间Markov 链、更新过程和鞅理论，构建了系统期望折扣总费用模型，并设计了交叉熵法确定最优库存策略。最后，通过仿真实验，分析了供应中断、净需求和系统参数，对最优控制策略和期望费用的影响。