本文針對需求呈隨機性且服從常態分配，進貨價格具數量折扣且允許缺貨之情況下，在考量額外積壓資金成本下，建構一數學模型以決定最適訂購量及安全存量水準，使總存貨成本最低。由於本研究所建構之存貨模型具多重變異性，因此除採一般最佳化分析技巧外，尚需經由電腦數值分析方法方能找出最佳解，最後再經由Hessian matrix驗證最適解之正確性。本文最後提出若干具體發現與結論，作為後續研究之參考。

This paper proposes a mathematical model to minimize total inventory cost with considering the additional capital holding cost under the conditions of random demand with normal distribution, quantity discounts for purchasing price and stockouts permitted. On this inventory model, due to multivariate conditions, this paper adopts the multivariate optimization technique and computerize numerical analysis method in solving the research problem. The solution is validated by applying Hessian matrix for the optimality. Finally, several concrete findings and conclusions were drawn for future studies.