具有非线性时间依赖持有及缺货成本的变质品库存控制研究

Research on Inventory Control of Deteriorating Items with Nonlinear Time Dependent Holding and Out-of-stock Cost

针对变质品的变质过程和缺货时部分滞后供给产生的缺货损失,考虑非线性变质过程和缺货成本,以变质品的单位时间利润最大化为目标构建库存控制模型。理论研究表明:有现货时间是缺货时间的增函数;在一定条件下,库存模型存在最优解,若不能满足该条件,则不允许缺货。回补订购量与市场需求率、等待时间的短缺滞后供给量敏感因子呈正相关,与等待时间敏感因子呈负相关。数值研究表明:当顾客对于等待容忍程度较高时,应采用饥饿营销策略,适当缩短有现货时间、延长缺货时间;持有成本弹性、短缺滞后供给量敏感因子、滞后供给成本和机会成本增大时均对该产品的回补订货周期产生负影响。

An inventory control model is constructed to maximize the profit per unit time of deteriorating products,with a focus on the deteriorating process of products and the loss caused by a partial lag supply in a stockout,in consideration of the nonlinear deteriorating process and the stockout cost. The theoretical research shows that the period of supplying products is an increasing function of the stockout time. Under certain conditions,there should be an optimal solution to the inventory model. If this condition can not be satisfied,there should not be any shortage. The quantity of order replenishment has a positive correlation with market demand rates and the sensitive factors of the lag supply caused by the latency time,and a negative correlation with the sensitive factors of the latency time. The numerical results show that when customers have a high tolerance for waiting,it is suggested to adopt the hunger marketing strategy to appropriately shorten the supplying time and prolong the stockout time;the order replenishment cycle of the product will be negatively affected by cost elasticity,the sensitive factors by the shortage lag supply,lag supply cost and the increasing opportunity cost.