在銷售體系中，當上游供應商提供現金折扣或信用期給下游的零售商時，下游零售商的定價通常會參考上游供應商所提供的付款條件來訂定。在過去相關的文獻中，較常看到在不同付款條件下研究補貨或訂價的問題。而在這裡所想要研究的目的主要在於當有二個價格互相競爭的零售商使用EOQ的存貨模式下，最大化上游供應商的利潤。我們在這提出了一個二階層的存貨模型，供應商提供給其中一個零售商現金折扣的付款條件，而另一個零售商則提供信用期的付款條件。在此模型中，零售價格會直接地影嚮到客戶端的購買行為。這篇文章的目的是希望幫供應商在上述所提的環境下，定義最佳的策略。 在解法方面，會利用Hessian matrix去證明供應商的利潤方程式是concave function。然後利用quasi-gradient的演算法去找到供應商的最佳解。最後在數值分析時我們發現當零售商的markup上昇時，供應商所提供的現金折扣或是信用期必須提高才能得到最大的利潤。而下降時則相反。 When a vendor (supplier) provides a cash discount or credit period policy, buyers will decide their prices and ordering policies accordingly. Previous researches often focused on the replenishment or pricing problems under different situations. The purpose of this research is to maximize vendor’s profit with the economic order quantity (EOQ) framework when both of the retailers have price competitive behaviors. We present a two-echelon inventory model in which the supplier offers one of its retailer cash discount, and the other credit period. The changes in retail prices directly affect customers’ purchase behavior. The objective of this research is to determine the optimal policies for the manufacturer under the situations described above. A solution method will use Hessian matrix to prove that profit function is concave, and find the order quantities and customer demand. Then, quasi-gradient algorithm will be developed to get supplier’s solution. We demonstrate that when retailer’s price markup is higher, and then the supplier should offer higher cash discount rate or longer credit period to maximize its profit.
