基于库存水平的ARMA(1,1)需求条件下目标库存水平优化方法

Optimization Model of Base Stock Level under Inventory-level-dependent ARMA(1,1) Demand

为降低企业库存成本,考虑ARMA(1,1)过程且受到库存水平影响的需求情形,建立定期库存策略的目标库存水平优化模型,提出该模型的求解算法,最后结合数例验证模型的实用性和可操作性,并分析需求自相关程度和需求对库存水平的依赖度、进货提前期等因素对目标库存量的影响,得出:目标库存量随进货提前期和需求自相关程度的提高而上升,若需求自相关程度越大,目标库存量提高得越快;若需求与库存量之间呈现多项式函数关系,目标库存量随需求对库存的依赖度提高而上升,且上升速度逐渐加快;若需求与库存量之间呈指数函数关系,目标库存水平随需求对库存的依赖度提高而基本不变.当需求对库存的依赖度较小时,目标库存水平呈现很小的下降趋势,反之,基本不变.

Based on a first order autoregressive and moving average （i. e. ARMA（1,1））, inventory-level-dependent demand, the optimization model of the base-stock level in periodic review strategy is developed. An algorithm is presented to find the solution to this model. At last, a numerical example is given to verify the availability of this model, as well as to examine the impacts of demand parameters, degree of demand dependence on the inventory and replenishment lead time on the base stock level. It can be shown from analysis that the base stock level is increasing in replenishment lead time and demand autocorrelation degree, the increasing rate of base stock level is increasing in demand autocorrelation degree. It can also be shown that,when the demand is a pesynomial function of the inventory level, the base stock level is increasing in the level of demand dependence on the inventory and the increase rate in the base stock level is also increasing in the level of demand dependence on the inventory. At last, it is shown that, when the demand is an exponential function of the inventory level, the base stock level maintains nearly stable as the degree of demand dependence on inventory increases, however, the base stock level presents a slight decline when the level of demand dependence on the inventory is lower.