退化性物品在性質上大致可以分成「即時退化」及「非即時退化」兩種，即時退化是指物品購入時就開始退化，使其無法保有原有的品質；而非即時退化是指物品在購入後，還能維持一段時間保有原有的品質，然後才開始退化，這類型的物品即稱為「非即時退化性物品」，也是本文主要探討的存貨物品。

　　再者，物品的需求率往往是變動的，消費者往往因貨架上存放較多數量的物品吸引其注意力而刺激購買意願；而有些物品則是因生命週期短，同質性商品又多，所以其需求率的降低速度非常的快速，譬如3C產品。因此，假設需求率固定不變是不符合現今多變化的市場環境。

　　另一方面，存貨物品會產生資金的積壓，以往所探討的存貨模型大多都是將物品銷售完畢後再訂購一批，但是對非即時退化性物品，在物品尚未完全銷售完畢前便以較便宜的價格出售，另再新訂購一批，對零售商而言，可能較為有利。因此，在本文裡，我們放寬期末存貨水準為零的條件，考慮允許期末還有存貨時，便以較低價格售出物品或容許缺貨待補。

　　總結，本文主要是探討非即時退化性物品並且放寬期末存貨條件的存貨系統，第二章是假設需求率與存貨水準有關，允許缺貨且部分欠撥，欠撥率為固定；第三章則是考慮需求率為時間的指數遞減函數，不允許缺貨。兩章的模型都以使得單位時間總利潤有最大值為目標，然後利用數理方法來求得最適解，並舉範例說明求解過程且對主要參數做敏感度分析。最後，第四章提出本文的結論及未來的研究方向。

Deteriorating items in the nature can be divided into "instantaneous deterioration" and "non-instantaneous deterioration". Instantaneous deteriorating is the item purchased immediately began to degenerate and can’t be retain the original quality. Non-instantaneous deterioration is not immediately degraded after the purchase and it still can maintain the original quality for some time then began to degenerate. This type of item is referred to as "non-instantaneous deteriorating items" and it is also the main items of the inventory we discuss in this paper.

　　The demand rate of item is changing. Consumers usually attracted by the large quantities of goods on shelves and stimulate purchase intention. And some items are due to short life cycle or homogeneous lead the demand rate of some items decrease rapidly. For example, 3C products , therefore, assuming the demand rate is fixed consistent does not meet current various market environment.

　　On the other hand, inventory could be the backlog of capital. Inventory models discussed previously ware that sell out of goods then reorder another lots. But for non-instantaneous deteriorating items, before selling out of goods we sell the goods of a lower price then reorder another lots. For retailers, it may be more beneficial for them. Therefore, in this paper, we relax the terminal condition of zero of inventory level at the end of cycle. Then we consider there are still some goods at the end of cycle sold with a lower price and allow shortages, backlogging in the model.

　　Summary, this paper is to explore the non-instantaneous deteriorating items and relax the terminal condition of the inventory system. In Chapter 2 we assume a demand rate and inventory levels related and we allow the shortages and the partial backorder, backorder rate is fixed. In Chapter 3 we consider the demand rate is a decreasing exponential function of time and don’t allow out of stock. Two chapters of the models in order to achieve the maximum total profit per unit time as the goal, and then use mathematical methods to get the optimal solution. Then we example illustrates both the value and sensitivity analysis of parameters and show the steps of solution. Finally, concluding remarks are made in Chapter 4 and future research directions are proposed.

目錄

目錄I
圖目錄III
表目錄IV
通用符號一覽表V
基本假設VI

第一章 緒論1
  1.1.  研究動機與目的1
  1.2.  相關文獻探討2
  1.3.  本文結構4
第二章 需求與存貨水準有關之非即時退化性物品在倉庫容量有限且放寬週
       期末存貨條件的最適補貨策略6
  2.1.  前言6
  2.2.  符號與假設7
  2.3.  模式的建立8
  2.4.  模式的求解24
  2.5.  數值範例45
  2.6.  小結49
第三章 需求與時間有關之非即時退化性物品在倉庫容量有限且放寬週期末
       存貨條件的最適補貨策略50
  3.1.  前言50
  3.2.  符號與假設51
  3.3.  模式的建立51
  3.4.  模式的求解60
  3.5.  數值範例73
  3.6.  小結77
第四章 結論及後續研究79
  4.1.  結論79
  4.2.  後續研究方向81
參考文獻83

圖目錄
圖2.1 週期結束時，存貨量為正值且T＜td的存貨系統9
圖2.2 週期結束時，存貨量為非負值且td≦T≦t1的存貨系統11
圖2.3 週期結束時存貨量為負值的存貨系統15
圖2.4 週期結束時的存貨量為非負值且T≦t1的存貨系統18
圖2.5 週期結束時的存貨量為負值的存貨系統21
圖3.1 週期結束時存貨量為正值且T＜td的存貨系統53
圖3.2 週期結束時存貨量為非負值且td≦T≦t1的存貨系統56
圖3.3 週期結束時存貨量為非負值且T≦t1＜td的存貨系統58

表目錄
表2.1 不同的參數值變動對於範例2.1最適解的影響46
表3.1 不同的參數值變動對於範例3.2最適解的影響75

參考文獻
中文文獻:
楊志德 (2007)。考慮非即時退化性物品的一些確定性存貨模式之研究，淡江大學管理科學研究所博士學位論文。

英文文獻:
[1]  Baker, R.C. and Urban, T.L. (1988). A deterministic inventory system with an　inventory-level-dependent demand rate. Journal of the Operational Research Society, 39, 823-831.
[2]  Chang, C.T. , Teng, J.T. and Goyal, S.K. (2010).Optimal replenishment　policies for non-instantaneous deteriorating items with stock-dependent 
demand. Int. J. Production Economics, 123,62-68.
[3]  Chang, H.J. and Dye, C.Y. (1999). An EOQ model for deteriorating items with time varying demand and partial backlogging. Journal of the Operational Research Society, 50, 1176-1182.
[4]  Covert, R.P. and Philip, G.C. (1973). An EOQ model for items with Weibull distribution deterioration. AIIE Transactions, 5, 323-326.
[5]  Dye, C.Y. (2007). Joint pricing and ordering policy for a deteriorating inventory with partial backlogging. Omega, 35(2),184-189.
[6]  Dye, C.Y. , Chang, H.J. and Teng, J.T. (2006). A deteriorating inventory model with time-varying demand and shortage dependent partial backlogging. European Journal of Operational Research, 172(2), 417-429.
[7]  Eilon, S. and Mallaya, R. V. (1966). Issuing and pricing policy of semi-perishables. Proceedings of the 4th International Conference on Operational Research,Wiley-Interscience, New York.
[8]  Geetha, K.V. and Uthayakumar, R. (2010). Economic design of an inventory policy for non-instantaneous deteriorating items under permissible delay in payments. Journal of Computational and Applied Mathematics,233,2492-2505.
[9]  Ghare, P.M. and Schrader, G.H. (1963). A model for exponentially decaying inventory system. Journal of Industrial Engineering, 14, 238-243.
[10] Gupta, R. and Vrat, P. (1986). Inventory model with multi-items under constraint systems for stock dependent consumption rate. Operations Research, 24, 41-42.
[11] Hadley, G. and Whitin, T.M. (1961). An optimal final inventory model.　Management Science, 7(2), 179-183.
[12] Harris, F. W. (1913). How many parts to make at once. Factory.The Magazine of Management, 10, 135-136.
[13] Ouyang, L. Y. and Dye, C. Y. (2005). An EOQ model for perishable items understock-dependent selling rate and time-dependent partial backlogging.
European Journal of Operational Research,163(3),776-783.
[14] Ouyang, L. Y. , Wu, K. S. and Yang, C. T. (2006). A study on an inventory　model for non-instantaneous deteriorating items with permissible delay in 
payments. Computers & Industrial Engineering, 51, 637-651.
[15] Pal, A.K., Bhunia, A.K. and Mukherjee, R.N. (2005). A marketing-oriented inventory model with three-component demand rate dependent on displayed stock level (DSL). Journal of the Operational Research Society, 56, 113-118.
[16] Pal, A.K., Bhunia, A.K. and Mukherjee, R.N. (2006). Optimal lot size model for deteriorating items with demand rate dependent on displayed stock level (DSL) 
and partial backordering. European Journal of Operational Research, 175(2),977-991.
[17] Papachristos, S. and Skouri, K. (2000). An optimal replenishment policy for deteriorating items with time-varying demand and partial-exponential type–backlogging. Operations Research Letters, 27, 175-184.
[18] Philip, G.C. (1974). A generalized EOQ model for items with Weibull distribution. AIIE Transactions, 6, 159-162.
[19] Sarker, B.R., Mukherjee, S. and Balan, C.V. (1997). An order-level lot size inventory model with inventory-level dependent demand and deterioration. International Journal of Production Economics, 48(3), 227-236.
[20] Silver, E.A., Pyke, D.F. and Peterson, R. (1998). Inventory Management and Production Planning and Scheduling (3rd edition), John Wiley & Sons.
[21] Shah, Y.K. (1977). An order-level lot size inventory model for deteriorating items. AIIE Transactions, 9, 108-112.
[22] Wang, S.P. (2002). An inventory replenishment policy for deteriorating items with shortages and partial backlogging. Computers & Operations Research, 29,2043-2051.
[23] Wee, H.M. (1992). Perishable commodities inventory policy with partial backordering. Chung Yuan Journal, 12, 191-198.
[24] Wee, H.M. (1995). A deterministic lot-size inventory model for deteriorating items with shortages and a declining market. Computers & Operations Research,22, 345-356.
[25] Wu, K.S. , Ouyang, L.Y. and Yang, C.T. (2005). An optimal replenishment　policy for non-instantaneous　deteriorating items with stock-dependent demand and partial backlogging demand. International Journal of Production Economics, 101, 369-384.
[26] Yang, H.L. (2005). A comparison among various partial backlogging inventory lot-size models for deteriorating items on the basis of maximum profit. International Journal of Production Economics, 96 (1), 119-128.
[27] Zhou, Y.W. and Lau, H.S. (2000). An economic lot-size model for deteriorating items with lot-size dependent replenishment cost and time-varying demand. Applied Mathematical Modelling, 24(10), 761-770.