提前期、构建成本和短缺量拖后率均可控的EOQ模型

传统库存模型通常将提前期和构建成本视为不可控制。事实上可以通过追加投资缩短提前期和降低构建成本。缺货期间,为减少订单丢失量和补偿顾客的损失,供应商会给予一定的价格折扣。现实库存系统中,容易得到需求的期望值和标准差,但较难得到其分布规律。基于此,考虑短缺量拖后率与价格折扣和缺货期间库存水平相关,提出了一种需求为任意分布且提前期和构建成本均可控的EOQ模型,证明了模型存在唯一最优解,给出了一种寻优算法。数值仿真分析表明,一般情况下,压缩提前期和降低构建成本能降低订购批量和安全库存,降低库存总成本;短缺量拖后系数和缺货概率对库存总成本影响较大,企业应尽量降低缺货概率,尤其在短缺量拖后系数较小时。

EOQ Model with Controllable Lead Time, Setup Cost and Backordering Rate

In traditional inventory model,lead time and setup cost are viewed as uncontrollable But,in practice,lead time can be shortened and set up cost can be reduced by added investment. During the short age,the supplier may of fer a price discount on the stock-outitem to compensate for the inconvenience of backorder and to prevent loss of orders. In practice,the mean and the standard variance of demand are a vailable,butitis hard to find its distribution. Under the assumption that backorder rate is dependent on inventory level and price discountin the period of shortage,this paper develops an EOQ model with controllable lead time and setup cost,in which the demand follows ageneral distribution The existence and uniqueness of optimal solution are proved and analgorithm searching for it is given. It is showed that order quantity,safety stock and inventory total cost can be generally reduced by shortening lead time and reducing set up cost. It is also showed that backordering parameter and probability of short age have a great impact on inventory total cost,so an enterprise should do its best to reduce probability of shortage,especially when backordering parameter is small.