Bayes Solution to Dynamic Inventory Models Under Unknown Demand Distribution
针对需求分布参数未知的定期盘点库存问题，利用贝叶斯方法将多维状态空间动态规划降为一维，并给出最优订货策略的显式形式，适用于消耗品和可修品两类模型。
This paper considers the periodic review inventory problem for which one or more parameters of the demand distribution are unknown with a known prior distribution chosen from the natural conjugate family. The Bayesian formulation of this problem results in a dynamic program with a multi-dimensional state space. Two models are analysed: the depletive inventory model of consumable items and the nondepletive model of reparable items. For both models and for some specific demand distributions, it is shown that the solution of the Bayesian model can be reduced to that of solving another dynamic program with a one-dimensional state space. Moreover, an explicit form for the optimal Bayesian ordering policy is given in each case.