允许缺货且具有随机缺陷率的EOQ模型研究

A Study on EOQ Model for Items with Random Defective Rate and Shortage Backordering

生产系统不完善、自然灾害、运输等因素对传统EOQ模型中产品质量100%合格的假设提出了巨大的挑战。本文考虑了含有缺陷率且允许缺货的库存模型,其中产品检验过程与补货过程同步进行,时间范围是无限的,每个订货周期可以看成是一个更新过程。通过建立具有随机缺陷率的模型,运用更新酬劳过程方法得到期望利润表达式,确定最优订购策略,并且运用具体算例进行了验证,最后通过实验仿真探讨了不同均值和方差下缺陷率对最优订购策略的影响,同时还研究了检验速率和单位持有成本对最优订购策略和期望总利润的影响。

External environment changes（e.g.mass customization,shorter time-to-market and outsourcing） have made product inventory management an important topic.Economic order quantity model（EOQ） is a classic inventory management model that has been widely used to address inventory problems.Although EOQ is a useful model,its practical applications are less useful because the model has the assumption that product quality is perfect.In reality,production systems are not perfect and are susceptible to many uncertain factors,including natural disasters,damages or breakages in transit,and defective products.Therefore,the traditional ordering strategy based on EOQ is not effective at determining the optimal order point and order quality.This paper develops an inventory model for products which contain defects and backorders,and uses two methods to determine the optimal ordering strategy.First,we establish the expected total profit expression per unit time by the traditional method and obtain optimal solutions to project inventory problems.Second,we introduce the renewal reward process theory.The optimal reorder point and order quantity are determined according to the theory.The optimal ordering strategy and the expected total profit per unit time are different,but both of them can be reduced to the same equations as those of classical EOQ model.After comparing different ordering strategies computed by these two methods,we discuss the influence of parameters and variables on optimal ordering and backorder quantity.Traditional factors,such as holding costs per unit time and fixed ordering costs,can affect the optimal ordering quantity.In addition to these traditional factors,backorder costs per unit time,demand rate per unit time,random number of defect items and screening rates per unit time can also affect the optimal ordering quantity,thereby affecting the formulation of an optimal ordering strategy.Optimal ordering quantity computed by these two methods will decrease when backorder costs per unit time（b） increase.This finding is consistent as that of the classical EOQ model.Another finding based on the renewal reward process method also shows that optimal ordering quantity will decrease when the variance in random percentage of defective items（p） is increased.This finding confirms with that of Markowitz portfolio theory.A series of simulation experiments are performed based on numerical examples to validate some results.The influences of different E [p]and Var [p]on the results of traditional method and renewal reward theory method are investigated.This investigation is conducted based on the assumption that the random defective fraction of each lot（p） has a uniform distribution.These numerical simulation results show that,if employed by the traditional method,the expected total profit per unit time will decrease,and the optimal order quantity and the optimal shortage will increase when the average value is E [p].In contrast,if employed by the renewal reward theory method,the optimal order quantity will increase,but the optimal shortage and the expected total profit per unit time will decrease.A further investigation shows that if employed by the traditional method the expected total profit per unit time will increase when the variance value Var [p]and the optimal order quantity decrease,and the shortage remains unchanged.If employed by the renewal reward theory method,the optimal order quantity and the corresponding expected total profit per unit time will increase;however,optimal shortage will remain unchanged.All these findings indicate that the renewal reward method is more effective than the traditional method at predicting the expected total profit per unit time,but not at the optimal order quantity.The effects of holding cost and screening rate on the optimal order quantity,optimum shortage and expected total profit per unit time are analyzed.In conclusion,the proposed model possesses more practical value than the classical EOQ model because our model can address issues related to the random percentage of defective items.