随机供应中断和退货环境下库存的应急控制

摘要

随机供应中断和退货环境下库存变化，失去传统上的单调性，呈现复杂的随机波动状态，从而，极大地增加了控制难度。为解决系统库存的短缺和超储问题，本文提出一个应急控制(包括应急采购和应急处理)策略。在库存水平的动态变化表示为L´evy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利润模型，并设计了交叉熵法确定最优控制策略。仿真结果表明，中断强度和类型及退货批次和批量，对最优应急处理水平和应急采购量均有较大影响。而退货类型仅影响最优应急处理水平，对最优应急采购量影响较小。%The evolution of the inventory level under stochastic supply disruptions and returns no longer varies mono-tonically but fluctuates stochastically, which makes it very difficult to control the inventory level. In order to solve the inventory shortage and overstock problems, a contingent control (including contingent sourcing and contingent disposal) policy is proposed in this paper. Under the condition that the inventory level process is expressed as a L´evy process, the expected total discounted profit model is derived by utilizing continuous-time Markov chain, renewal process and martingale theorems. Subsequently, the cross-entropy method is designed to obtain the optimal control policy. Numerical results show that the intensity and the types of disruptions, as well as the arrival rates and the batch sizes of returns are critical determinants of the optimal contingent disposal level and contingent sourcing size. However, the types of returns have big impacts on the optimal contingent disposal level, but little impacts on the optimal contingent sourcing size.