本研究探討缺貨時欠撥(backorders)及銷售損失(lost-sales)的混合存貨说型，而欠撥率爲一隨機變数；並且考量在數量折扣與額外積壓資金交互作爪下，對存货策略及成本的影響。文中的訂購數量(order quantity)、前置時間(lead time)和請購點(reorder point)皆爲決策變数。本文首先假設前置時間內的需求服從常態分配；接著放寬此一設定，而僅假設前置時間內需求的平均数(mean)及變異數(variance)為已知。對此兩個模型各研擬出一套演算程序以求出最佳解。另外，文中亦討論參數變動對本模型及最適解的影響。
This paper investigates a mixture inventory model with backorders and lost sales, and the backorder rate is a random variable. We consider the effect of both quantity discounts and additional holding capital on inventory model, in which order quantity, reorder point, and lead time are viewed as the decision variables. 1n this study, we first assume that the demand of lead time follows a normal distribution, and then relax the assumption about the form of the distribution function of lead time demand and only assume that the mean and variance are known. We develop an algorithm procedure to find the optimal solution for each case. Furthermore, the sensitivity analysis is also performed.