基于MCMC的随机库存系统中提前期需求分布的计算

在需求和提前期均是随机的库存系统中,提前期需求的分布是由提前期分布与需求分布复合而成的,这个复合分布的计算通常是困难的。本文采用基于Gibbs抽样的马尔科夫链蒙特卡洛(MCMC,Markov chain Monte Carlo)方法,抽取条件分布样本作为提前期需求分布的样本,通过样本来计算提前期需求分布密度、服务水平和损失函数。这种方法避免了直接求解复杂积分计算上的困难,也克服了近似分布拟合偏差过大的问题,有效地解决了随机需求与随机提前期的复杂库存系统中提前期需求确定问题。理论与数值分析结果表明:与现有方法相比较,基于MCMC的方法具有计算简便、拟合精度高、通用性好等特点。

Computing Lead Time Demand Distribution of Stochastic Inventory System Based MCMC Method

The derivation of lead time demand distribution of an inventory system when both the demand and lead time are random variables,resulted in the compound distribution,which is a challenging analytic task.A Markov chain Monte Carlo method with Gibbs sampler is proposed to sample from conditional density as from lead time demand distribution;and based on the samples,lead time demand distribution density,service level and loss function are computed.The mentioned method overcomes computational difficulties in computing a complex integral;it overcomes biased estimation by using approximation solutions;and it figures out the lead time demand distribution of complex inventory system when both the demand and lead time are random variables effectively.The analysis results in theory and in numerical instances show that MCMC is a simple,unbiased and universal way for calculating lead time demand distribution.