在本研究我們提出兩個之退化性存貨模型並考慮隨機性需求與固定壽命。由於退化性商品在我們日常生活中隨處可見，所以已經有很許多學者研究關於此議題。而退化性商品需再在到期之前被販售掉或者被使用掉，因此隨著使用壽命的問題，我們也須考慮商品到期日的問題，以避免企業承擔不必要的損失。大部分的存貨模型都假設在確定性方程式或常數性的需求，但這是不合理的，因為現實生活中是需求是不可預測的。因此我們考慮上述因素提出兩種存貨政策。第一個存貨政策是不允許缺貨，也就是訂單會在庫存耗盡時迅速補貨。第二個存貨政策是允許缺貨，也就是說我們只能在到期日補貨，假如到期日庫存已提早耗盡就會發生缺貨。由於隨機性需求的影響，我們必需在每個模型裡考慮兩種方案。第一方案是當需求疲乏時，存貨可能會有剩餘品，因此這些商品需要報廢。第二方案是當需求旺盛時，由於存貨在到期日之前提早耗盡，在這個狀況下模型二會產生缺貨。最後，為了求解兩模型本研究為這兩種模型提出了近似解並考慮上述狀況，結果顯示我們的近似解非常接近真實最佳解，並且提出最佳單位時間利潤之敏感度分析。

This paper deals with two specific inventory models for deteriorating items with a stochastic demand rate and a fixed shelf lifetime. Many researchers have been studied deterioration phenomenon as the deteriorating items always appear ubiquitously. In practice, the expiration date is a problem of deteriorating items that must be sold before their fixed shelf lifetime, or that only can be used within a certain period after being unpacked. As a result, consideration of the expiry date could help enterprise to avoid profit loss without waste of the orders. Most of current inventory models dealing with deterioration would assume a certain or a constant demand function. This is certainly unreasonable in a prevailing market of stochastic demand which conforms to our daily reality, therefore stochastic demand must be considered. Here, we present ordering policies for two such inventory models. In model I, ordering would be immediately replenished when the inventory level drops to zero even before the expiration date. Namely, the stock shortage is not allowed. In model II, shortage is allowed and the items are not backlogged even after the stock depletes. Only at the expiration date can the replenishment arrived instantaneously. Furthermore, because of the effect of the stochastic demand condition, we must consider two cases for each model in this paper. In the first case, due to lack of demand, the stock remains even at expiration date. The remainder is assumed to be discarded with cost. In the second case, the stock depletes earlier before the expiration date during the period of high demand. In this case, model II occurs shortage until replenishment arrived at expiration date. Finally, we provide the approximated solution for optimal ordering quantity for both models. In order to maximize expected relevant total profit, we also present sensitivity analysis of the expected total relevant profit influenced by prices, expiration dates …etc. by the help of numerical examples. It shows that our approximated solutions from the assumed models that mentioned above gives conditions and the results very close to the optimal solution obtained from computation. Moreover, these results reveal the impact of various parameters on the optimal policy and the profit.

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