在一般的商業交易行為中，我們發現到零售商基於增加市場占有率及降低未來需求的估計誤差等原因會提供顧客預購的價格折扣。此外，以往文獻通常假設需求率為一固定常數。然而由物品的生命週期看來，需求只有在穩定期才為一常數，通常是與時間有關。當需求對時間具有敏感性時，零售商如何決定物品的預購折扣率和訂購策略使其總利潤有最大值是值得探討的課題。
    另外，我們也發現到：供應商基於某些原因如欲刺激零售商購買或買賣雙商簽訂供應鏈合約，會嘗試提供顧客信用交易等優惠。然而，事實上，零售商也可能提供顧客信用交易期限，以刺激需求來增加銷售收入。因此，我們考慮了供應商提供給零售商一個信用交易期限M ，同時零售商亦提供給顧客一個信用交易期限N，並在 N < M假設下，進一步探討零售商最適訂購量存貨模型。
    再者，傳統EOQ模型大都假設零售商沒有倉庫容量限制，使零售商可以任意的訂購，事實上，自有倉庫是有容量限制的，當訂購的物品數量超過自有倉庫的容量限制時，零售商應考慮外租倉庫來儲存物品。以往文獻探討欠撥率時，顧客對於上游零售商的存貨水準
或是訂購週期有充分的訊息與瞭解前提下，顧客會因等候時間或負的存貨水準而影響其等候意願。因此，將假設單位時間缺貨成本為時間的線性函數，表示零售商負的存貨水準並不會影響到顧客的購買產品的忠誠度。即每單位的缺貨成本與等候時間長短有關，使得模型的應用更能符合實際情況。
    本文係探討一些預先訂購物品的存貨系統，全文包括了三個存貨模型，第二章，探討在允許信用交易與預先訂購下之退化性物品的存貨模型。與之前文獻不同的是，假設與時間有關需求。第三章延續第二章的研究，探討允許預先訂購與在有限計畫期間內需求隨時間變動之最適訂購策略，並提出一個演算法協助零售商尋找最佳補貨次數與最適訂購週期。第四章則在探討需求率為固定常數且預先訂購的兩倉庫退化性物品存貨模式，不同以往的是假設單位時間缺貨成本為時間的線性函數且部分欠撥。進一步我們利用數理方法分別得到所提三種存貨模式最適解存在的充分且必要條件，並分別舉例說明其求解過程。最後，第五章為結論，並對本文各章所建構的存貨模型做一總結，同時提出未來的研究方向。

In business dealing, there exists many factors like advance booking discount to make retailers buy goods early. For companies, the advance booking discount strategy is common and useful in reality to decrease the estimation error in demand and to increase the market share. Furthermore, in real life, the demand is usually influenced by time. In the growth stage of a product life cycle, the demand rate can be well approximated by a linear form or exponential form. The retailer sells the product through an advance booking discount and aiming to optimize price discount and replenishment cycle time to maximize total profit per unit time.
Next, the supplier would offer the retailer a delay period M and the retailer could sell the goods and accumulate revenue and earn interest within the trade credit period. Furthermore, the retailer also offer the customer a delay period N to stimulate his/her customer demand to develop the retailer’s replenishment model(N < M ). Under these conditions, we model the retailer’s inventory system as a cost minimization problem to determine the retailer’s optimal ordering policies.
Further, the general assumption in classical inventory models is that the organization owns a single warehouse without capacity limitation. In practice, while a large stock is to be held, due to the limited capacity of the owned warehouse (denoted by OW), one additional warehouse is required. This additional warehouse may be a rented warehouse (denoted by RW), which is assumed to be available with abundant capacity. However, the backlogging rate in classical inventory models based on the waiting time are realistic only if the supply chain between the retailer parties and the customer parties has enabled share information through the well channel partnership. 
This thesis is consisted of five chapters. In Chapter 2, we first explores a generalized inventory control system for deteriorating items with time-varying demand under advance booking discount and two-echelon trade credits. In Chapter 3, we extend Chapter 2’s model and then propose a finite time horizon inventory model for deteriorating items with time-varying demand through an ABD program. We further simplify the search process by providing an intuitively good starting value for the optimal number of replenishments and the optimal replenishment cycle time. In Chapter 4, we present a deterministic inventory model for deteriorating items with two warehouses under ABD program.
Moreover, we assume that the backorder cost per unit time is a linearly function and partial backlogging δ . The necessary and sufficient conditions of the existence and uniqueness of the optimal solutions for the three models are shown. Some numerical examples are used to illustrate the three model and conclude the thesis with suggestions for possible future research.

目錄 i

表目錄 iv
圖目錄  v
使用符號一覽表 vi
第一章 續論 1
1.1 研究動機與目的 1
1.2 相關文獻探討 2
1.2.1 信用交易 2
1.2.2 與時間有關需求 3
1.2.3 預先訂購 4
1.2.4 兩倉庫存貨模型 5
1.3 本文結構 6
第二章 在允許信用交易與預先訂購下之退化性商品的存貨模型 8
2.1 前言 8
2.2 符號說明與假設 9
2.3 模式的建立 10
2.4 情況1.之模式求解 19
2.5 求解過程 20
2.6 數值範例 23
第三章 允許預先訂購與在有限計畫期間內需求隨時間變動之最適訂購策略 25
3.1 前言 25
3.2 符號說明與假設 25
3.3 模式的建立 26
3.4 模式求解 28
3.5 演算法 30
3.6 數值範例 33
第四章 需求率為固定常數且預先訂購的兩倉庫退化性商品存貨模式 35
4.1 前言 35
4.2 符號說明與假設 35
4.3 模式的建立 37
4.4 模式求解 42
4.5 自有倉庫無容量限制的存貨模型 51
4.6 數值範例 56
第五章 結論 58
5.1 主要研究成果 58
5.2 未來研究方向 60
參考文獻 61
附錄 A 72
附錄 B 74
附錄 C 75
附錄 D 76
附錄 E 78
附錄 F 80
附錄 G 81
附錄 H 83
表目錄
3.1 例題1之求解程序列表 34
4.1 P(to; ts)和Pow(to; ts)數值範例結果 56
4.2 P(to; ts)和Pnon-ABD(to; ts)數值範例結果 57
4.3 參數δ變動對最適總利潤的影響 57
4.4 參數cb變動對最適總利潤的影響 57
圖目錄
1.1 本文結構流程圖 7
2.1 存貨水準與產生利息之銷售量是意圖 11
3.1 Nelder-Mead演算法示意圖 32

[1] P.L. Abad (1996), "Optimal pricing and lot sizing under conditions of perishability and partial backordering, ", Management Science,42,1093-1104.
[2] P.L. Abad (2001), "Optimal price and order size for a reseller under partial backordering", Computers and Operations Research,28,53-65.
[3] S.P. Aggarwal (1978), "A note on an order level inventory model for a system with constant rate of deterioration", Opsearch,15,184-187.
[4] S.P. Aggarwal and C.K. Jaggi (1989), "Ordering policy for decaying inventory", International Journal of Systems Science,20,151-155.
[5] S.P. Aggarwal and C.K. Jaggi (1995), "Ordering policies of deteriorating items under permissible delay in payments ", Opsearch,46,658-662.
[6] K.A. Arrow, T.E. Harris and J. Marschak (1951), "Optimal inventory policy", Econometrica,19,250-272.
[7] K.A. Arrow, S. Karlin and H. Scarf (1958), "Studies in the mathematical theory of inventory and production", Standford Univ. Press, 368-401.
[8] F.J. Arcelus and Srinivasan G. (1993), "Integrating working capital decisions", The Engineering Economist,39, 1-15.
[9] L.C. Barbosa, M. Friedman (1978), "Deterministic inventory lot size models-a general root law", Management Science,24, 819-826.
[10] R.E. Bellmann(1957), "Dynamic Programming", Princeton University Press, Princeton, N.J.
[11] P.P. Belobaba (1989), "Application of a probabilistic decision model to airline seat inventory control", Operational Research,37, 183-197.
[12] L. Benkherouf. (1995), "On an inventory model with deteriorating items and decreasing time-varying demand and shortages", European Journal of Operational Research,86,293-299.
[13] L. Benkherouf (1997), "A deterministic order level inventory model for deteriorating items with two storage facilities", International Journal of Production Economics,
48, 167-175.
[14] J.T. Buchanan (1980), "Alternative solution methods for the inventory replenishment problem under increasing demand", Journal of Operational Research Society,31, 615-
620.
[15] A.K. Bhunia, M. Maiti (1994), "A two warehouse inventory model for a linear trend in demand", Opsearch,31, 318-329.
[16] A.K. Bhunia, M. Maiti (1998), "A two-warehouse inventory model for deteriorating items with a linear trend in demand and shortages", Journal of the Operational
Research Society, 49, 287-292.
[17] C.T. Chang, L.Y. Ouyang and J.T. Teng (2003), "An EOQ model for deteriorating items under supplier credits linked to ordering quantity", Applied Mathematical Modelling,27, 983-996.
[18] H.C. Chang (2004), "An application of fuzzy sets theory to the EOQ model with imperfect quality items", Computers and Operations Research,31, 2079-2092.
[19] H.J. Chang and C.Y. Dye (1999), "An EOQ model for deteriorating items with time varying demand and partial backlogging", Journal of the Operational Research
Society, 50, 1176-1182.
[20] H. J. Chang and C.Y. Dye (2001), "An inventory model for deteriorating items with partial backlogging and permissible delay in payments", International Journal
of Systems Science,32, 345-352.
[21] T. Chakrabarty, B.C. Giri and K.S. Chaudhuri(1998), "An EOQ model for items with Weibull distribution deterioration, shortages and trended demand: an extension
of Philip's model", Computers and Operations Research,25, 649-657.
[22] J.M.Chen (1998), "An inventory model for deteriorating items with time-proportional demand and shortages under inflation and time discounting", International Journal of Production Economics,55, 21-30.
[23] L.H. Chen and Y.C. Chen (2008), "A newsboy problem with a simple reservation arrangement", Computers and Industrial Engineering,Article in press.
[24] P. Chu, K.L. Yang, S.K. Liang, T. Niu (2004), "Note on inventory model with a mixture of back orders and lost sales", European Journal of Operational Research,159,
470-475.
[25] R.B. Covert, G.S. Philip (1973), An EOQ model with Weibull distribution deterio-
ration", AIIE Transactions,5, 323-326.
[26] U. Dave, L. K. Patel (1981), (T, Si) policy inventory model for deteriorating items
with time proportional demand", Journal of the Operational Research Society, 32,
137-142.
[27] U. Dave, (1988), "On the EOQ models with two levels of storage", Opsearch,25,190-196.
[28] C.Y. Dye and L.Y. Ouyang, (2005), "An EOQ model for perishable items under stock-dependent selling rate and time-dependent partial backlogging", European Journal of
Operational Research, 163, 776-783.
[29] C.Y. Dye, L.Y. Ouyang and T.P. Hsieh (2007), "Deterministic inventory model for
deteriorating items with capacity constraint and time proportional backlogging rate", European Journal of Operational Research,178, 789-807.
[30] A. Dvoretzky, J. Kiefer and J. Wolfowitz (1952), "The inventory problem: II.case of unknown distributions of demand", Econometrica,20, 450-466.
[31] P.M. Ghare, G.H. Schrder (1963), "A model for an exponentially decaying inventory", Journal of Industrial Engineering,14, 238-243.
[32] S.K. Goyal (1985), "Economic order quantity under conditions of permissible delay in payments", Journal of Operational Research Society,36, 335-338.
[33] A. Goswami, K.S. Chaudhuri (1991), "An EOQ Model for Deteriorating Items with Shortages and a Linear Trend in Demand ", Journal of the Operational Research
Society,42, 1105-1110.
[34] S.K. Goyal, M.A. Hariga and A. Alyan (1996), "The trended inventory lot sizing problem with shortages under a new replenishment policy", Journal of the Operational Research Society,47, 1286-1295.
[35] A. Goswami, K.S. Chaudhuri (1998), "On an inventory model with two levels of storage and stock-dependent demand rate", International Journal of Systems Sci-
ences,29, 249-254.
[36] S.K. Goyal, B.C. Giri (2001), "Recent trends in modeling of deteriorating inventory", European Journal of Operational Research,134, 1-16.
[37] F.W. Harris (1915), "Operations and costs", Chicago.
[38] R.V. Hartley (1976), "Operations Research-A Managerial Emphasis", Good Year Publishing Company, California,315-317.
[39] M. Hariga (1996), "Optimal EOQ models for deteriorating items with time-varying demand", Journal of the Operational Research Society,47, 1228-1246.
[40] R.J. Henery (1979), "Inventory replenishment policy for increasing demand ", Journal of the Operational Research Society,30, 611-176.
[41] Y.F. Huang (2003), "Optimal retailer's ordering policies in the EOQ model under trade credit financing", Journal of the Operational Research Society,54, 1011-1015.
[42] W.T. Hu, S.L. Kim and A. Banerjee, (2008), "An inventory model with partial backordering and unit backorder cost linearly increasing with the waiting time ",
European Journal of Operational Research, Article in press.
[43] A.M. Jamal, B.R. Sarker and S. Wang (1997), "An ordering policy for deteriorating items with allowable shortage and permissible delay in payment", Journal of
Operational Research Society,48, 826-833.
[44] S. Kar, A.K. Bhunia, M. Maiti (2001) "Deterministic inventory model with two levels of storage, a linear trend in demand and a fixed time horizon ", Computers and Operations Research,28, 1315-1331.
[45] S.E. Kimes (1989), "Yield management: a tool for capacity-constrained service firms", Journal of Operational Management,8, 348-363.
[46] J.S. Kim, H. Hwang and S.W. Shinn (1995), "An optimal credit policy to increase supplier's profits with price dependent demand functions", Production Planning and
Control,6, 45-50.
[47] M. Khouja and A. Mehrez (1996),"Optimal inventory policy under different supplier credit policies", Journal of Manufacturing System, 15, 334-339.
[48] K. McCardle, K. Rajaram, C.S. Tang (2004), "Advance booking discount programs under retail competition", Management Science,50, 701-708.
[49] T.A. Murdeshwar, Y.S. Sathe (1985), "Some aspects of lot size model with two levels of storage", Opsearch,22, 255-262.
[50] T.M. Murdeshwar (1988), "Inventory replenishment policy for linearly increasing demand considering shortages-An optimal solution ", Journal of the Operational Research Society,39, 687-692.
[51] L.Y. Ouyang, T.P. Heish, C.Y. Dye, H.C. Chang (2003), "An inventory model for deteriorating items with stock-dependent demand under the conditions of inflation and time-value of Money", The Engineering Economist,48, 52-68.
[52] L.Y. Ouyang, J.T. Teng, K.W. Chuang and B.R. Chuang (2005), "Optimal inventory policy with noninstantaneous receipt under trade credit", International Journal of Production Economics,98, 290-300.
[53] G. Padmanabhan, P. Vrat (1990), "Inventory model with a mixture of back orders and lost sales", International Journal of Systems Science,21, 1721-1726.
[54] T.P.M. Pakkala, K.K. Achary (1992a), "Discrete time inventory model for deteriorating items with two warehouses", Opsearch , 29, 90-103.
[55] T.P.M. Pakkala, K.K. Achary (1992b), "A deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate", European Journal of Operational Research,57, 71-76.
[56] G. Padmanabhan, P. Vrat (1995), "EOQ models for perishable items under stock dependent selling rate", European Journal of Operational Research,86, 281-292.
[57] S. Papachristos and K. Skouri (2000), "An optimal replenishment policy for deteriorating items with time-varying demand and partial-exponential type backlogging",
Operations Research Letters,27, 175-184.
[58] G.C. Philip, (1974), "A generalized EOQ model for items with Weibull distribution deterioration", AIIE Transactions,6, 159-162.
[59] R.I. Phelps (1980), "Optimal inventory rule for a linear trend in demand with a constant replenishment period", Journal of the Operational Research Society,31, 439-442.
[60] E. Ritchie. (1984), "The EOQ for linear increasing demand: a simple optimal solution", Journal of the Operational Research Society, 35, 949-952.
[61] K.V.S. Sarma (1983), "A deterministic inventory model with two level of storage and an optimum release rule", Opsearch, 20, 175-180.
[62] R.S. Sachan (1984), "On (T, Si) policy inventory model for deteriorating items with time proportional demand", Journal of the Operational Research Society,35, 1013-1019.
[63] K.V.S. Sarma (1987), "A deterministic order level inventory model for deteriorating items with two storage facilities", European Journal of Operational Research,29, 70-73.
[64] M.K. Salameh, N.E. Abboud, A.N. El-Kassar and R.E. Ghattas (2003), "Continuous review inventory model with delay in payments", International Journal of Production
Economics,85, 91-95.
[65] E.A. Silver (1979), "A simple inventory replenishment decision rule for a linear trend in demand", Journal of the Operational Research Society,30, 71-75.
[66] V.R. Shah, N.C. Patel and D.K. Shah (1988), "Economic ordering quantity when delay in payments of order and shortages are permitted", Gujarat Statistical Review,15,52-56.
[67] J.T. Teng (1994), "A note on inventory for replenishment policy for increasing demand", Journal of the Operational Research Society, 45, 1335-1337.
[68] J.T. Teng, M.S. Chern, H.L. Yang, Y.J.Wang (1999), "Deterministic lot-size inventory models with shortages and deterioration for fluctuating demand", Operations Research Letters,24, 65-72.
[69] J.T. Teng (2002), "On the economic order quantity under conditions of permissible delay in payments", Journal of the Operational Research Society,53, 915-918.
[70] J.T. Teng, H.J. Chang, C.Y. Dye, C.H. Hung (2002), "An optimal replenishment policy for deteriorating items with time-varying demand and partial backlogging",
Operations Research Letters , 30, 387-393.
[71] J.T. Teng, C.T. Chang and S.K. Goyal (2005), "Optimal pricing and ordering policy under permissible delay in payments", International Journal of Production Economics, 97, 121-129.
[72] J.T. Teng, L.Y. Ouyang and L.H. Chen (2006), "Optimal manufacturer's pricing and lot-sizing policies under trade credit financing", International Transactions in Operational Research, 13, 1-14.
[73] Y.C. Tsao (2008), "Retailer's Optimal Ordering and Discounting Policies under Advance Sales Discount and Trade Credits", Computers and Industrial Engineer-
ing,Article in press.
[74] L.R. Weatherford and P.E. Pfeifer (1994), "The Economic Value of Using Advance Booking of Oders", Journal of management science,22, 105-111.
[75] H.M. Wee (1995), "Joint pricing and replenishment policy for deteriorating inventory with declining market", International Journal of Production Economics, 40, 163-171.
[76] H.M. Wee (1995), "A deterministic lot-size inventory model for deteriorating items with shortages and a declining market", Computers and Operations Research, 22, 345-356.
[77] H.M. Wee (1997), "A replenishment policy for items with a price-dependent demand and a varying rate of deterioration", Production Planning and Control, 8, 494-499.
[78] R.H. Wilson (1934), "A scientific routine for stock control", Harvard Business Review,3, 116-128.
[79] H.L. Yang, J.T. Teng, M.S. Chern (2001), "Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand", Naval Research Logistics, 48, 144-158.
[80] H.L. Yang (2004), "Two-warehouse inventory models for deteriorating items with shortages under inflation", European Journal of Operational Research, 157, 344-356.
[81] P.S. You (2006), "Ordering and pricing of service products in an advance sales system with price-dependent demand", European Journal of Operational Research, 170, 57-71.
[82] P.S. You and M.T. Wu (2007), "Optimal ordering and pricing policy for an inventory system with order cancellations", OR Spectrum, 29, 661-679.
[83] C.T. Yang (2008), "The optimal order and payment policies for deteriorating items in discount cash flows analysis under the alternatives of conditionally permissible delay in payments and cash discount ",TOP.
[84] Y.W. Zhou (2003), "A multi-warehouse inventory model for items with time-varying demand and shortages", Computers and Operations Research, 30, 2115-2134.
[85] Y.W. Zhou and J. Minab (2009), "A perishable inventory model under stockependent selling rate and shortagedependent partial backlogging with capacity constraint", International Journal of Systems Science, 40, 33-44.