服务多类需求串行供应链的最优控制策略

Optimal control of a series system with stochastic leadtime and multiple demand classes

研究由一系列生产环节采用串行方式组成多级供应链的最优控制策略.在此供应链中,原材料经过各级生产环节顺序加工形成最终产品.各级生产环节的加工时间服从随机分布.对最终产品存在多类随机需求.在每个时刻,管理者需要决定:1)是否该启动某个生产环节的生产;2)当有需求到达时,是否该满足此需求.管理者期望系统运行的总期望折扣成本最小.构造了该系统的马尔可夫决策模型并深入研究了其最优控制策略及其动态协同特性.在生产策略方面,证明系统的最优生产策略就是对各级生产环节采用动态的基本库存策略.该策略的动态协同特性主要体现在各级生产环节的最优基本库存水平受其他生产环节的库存水平影响.在产品分配方面,证明系统的最优分配策略是动态配给策略.该策略的动态协同特性主要体现在每类随机需求最优配给水平受各级生产环节的库存水平影响.

A multi stage series system with stochastic lead time and multiple demand classes is considered. Starting from the raw materials, the product is processed in the system stage by stage. ＋There exist multiple demand classes for the final product. At each time epoch, the system manager must decide （ 1 ） whether or not to activate the production process at a stage and （2）, should demand from a particular class arise, whether or not to satisfy it from existing inventory. The system manager seeks to minimize the total discounted cost. The problem is formulated as a Markov decision process. Based on the formulation, the structure of the optimal policy is characterized. For the production policy, a state-dependent base-stock policy for each stage is optimal. It is shown that the optimal base stock level of one stage is non-increasing in the inventory level in its＇ downstream stages and non-decreasing in the inventory level in its＇ upstream stages. For the inventory allocation policy, a state-dependent rationing policy is optimal. It is shown that the optimal rationing level is non-decreasing in the inventory level in upstream stages.