在物料管理方面，如何適時、適量的控制存貨，以達到最低的總成本，是任一企業最為注重的問題。但是很明顯的發現，有非常多的物料都是具有損耗或退流行的性質，例如生鮮食品、電子零件、香水、攝影底片、放射性物質、週期性商品等等；而製造商應就整體環境考量，以決定最有利的製造方式。基於上述的理由，本研究將分別針對物料具有週期性或是一般損耗性來進行研究探討。
首先，我們針對週期性物料，建構出二階存貨模式之製造商的利潤函數，並對於此函數進行傳統的最佳解分析，以期獲得製造商的生產數量以及原物料的訂購週期。根據報童模式，且在零售商的需求量為一常態分配的前提之下，獲得製造商的利潤函數最佳解之充分與必要條件；由於，無法獲得唯一組解，所以，透過敏感度分析以及其在管理上的含義，對於所獲得最佳解之必要條件進行探討並解釋之。
其次，針對二階損耗性物料的特性，建構出固定週期時間的成本函數；並對於此成本函數進行最佳解分析，獲得固定週期時間模式有唯一組解；再透過敏感度分析獲得一些管理上的含義，並對於零售商願意加入此整合模式加以探討。
最後，考慮物料具有損耗性，且允許完全補貨下，且對於上述模式之固定週期時間給予放寬，建構出非固定週期時間的成本函數；並對於此成本函數進行最佳解分析，在固定補貨次數下，可以獲得最低成本的製造時間點；再透過敏感度分析獲取一些管理上的含義。

The control and maintenance of physical goods inventories is a common problem to all enterprises in any sectors. Two fundamental questions in controlling the inventory of any physical goods are when to replenish the inventory and how much to order for replenishment. Previous studies did not consider the deterioration property of the inventory. Nevertheless, all the items on earth deteriorate eventually, and some of which deteriorate significantly, such as certain types of food, photographic films, electronic components and radioactive substances, periodically products, etc. Hence the research developed a two-echelon inventory model for a periodical commodity and a two-echelon inventory model with deteriorating items, respectively.
First of all, we proposed a two-echelon inventory model for a periodical commodity, in which the market and manufacturing channels are combined. This model can be used to solve the production policy and the order policies of the raw materials for the manufacturer. By assuming that the retailers’ demand obeys normal distribution and that the retailer makes orders according to the Newsboy Model, we derive the necessary and sufficient conditions for the optimal solution of production size, wholesale price, and replenishment cycle of raw materials for the manufacturer. Also, the necessary condition is explored in order to obtain managerial insights and economic implications based on numerical examples and sensitivity analysis.
Second, a cooperative inventory policy between suppliers and buyers is also proposed. We consider the case of deteriorating items, and permit the completed backorder with fixed service rate in the problem. We directly solve the problem in a specified planning horizon and present a procedure to find the optimal solution. Numerical examples are provided to illustrate the solution procedure. In addition, the cooperative policies between suppliers and buyers are discussed.
Finally, we solve the problem without the condition of equal replenishments periods during a specified planning horizon and present a procedure to find the optimal solution. Numerical examples are provided to illustrate the solution procedure and the cooperative policies between the suppliers and the buyers are also discussed. Furthermore, the results also show that the optimal cost of the model is lower than that of the model of assuming equal replenishments periods.

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