企業管理的主要目標在減少成本與改善品質。實際上，降低存貨是控制成本最有效的方法。傳統的經濟訂購量模式，供應商交貨給零售商，零售商即需付款給供應商，然而實際商場交易，供應商往往會給予零售商一段固定延後付款期限或現金折扣優惠。故競爭環境下信用交易對企業存貨訂購策略的影響已成為學者注意的重要議題。
本文考量市場實際交易狀況，發展允許延遲付款條件下之存貨補充模式與最佳訂購策略。本研究共發展三種不同的訂購模式，首先，由於大多數的交易模式僅考慮供應商給予批發商、零售商延後付款條件，但實際情況，批發商也會給予下游顧客延後付款期限。本論文第三章推導出訂購量大於某一最低量時，二階信用交易條件下批發商之最佳經濟訂購策略。其次，本論文第四章假設零售商的訂購量大於某一最低量時，供應商提供延後付款與現金折扣兩種優惠付款條件給零售商選擇，並就上述情況的存貨系統求得最佳訂購策略。另外，傳統的經濟訂購量模式大都假設產品是完美且補充率無限大，然而，此一狀況很少存在實際的生產環境，本論文第五章提出二階信用交易條件且存貨有瑕疵和有限補充率下之存貨訂購模式。
本研究共提供三個存貨系統模式，每個存貨系統皆導出其每年總相關成本函數或利潤函數為目標函數，然後探討目標函數的性質，推導出各種情況之訂購策略的決策法則，再透過敏感度分析以瞭解各參數對存貨模式的影響。最後，舉個案範例驗證並加以說明其管理意涵。

The major goals in manufacturing environments are minimizing costs and improving overall quality. In fact, reducing inventory is the often the most effective way to control production costs. The basic economic order quantity (EOQ) model assumes that the buyer must pay as soon as the shipment is received. However, a common practice in various industries is to provide the buyer with either a cash discount or a permissible delay in payment. The models for inventory replenishment polices under trade credit have widely received the attention of many researchers. The influences of trade credit have been shown to be an important issue in inventory policies for a company to be competitive.
This article considers some realistic conditions to develop inventory replenishment models and determine the optimal order policies under permissible delay in payments. This paper develops three different models, which reflect the real trade credit situation. First, most studies of trade credit model have only considered suppliers offering the wholesaler a grace period. In practice, wholesalers often extend a fixed credit period to downstream customers as well. In chapter 3, this study is proposed to determine the optimal replenishment decisions under two levels of trade credit policy if the purchasers order quantity is greater than or equal to a predetermined quantity. Secondly, in chapter 4, this model is proposed to an inventory model under trade credit, in which the supplier provides not only a cash discount but also a permissible delay to the buyer if the order quantity is greater than or equal to a predetermined quantity. Additionally, the traditional inventory of the economic order quantity model assumes perfect items in an ordered lot and an infinite replenishment rate. However, such conditions are rare in actual production environments. In Chapter 5, this study therefore proposes a production model for a lot-size inventory system with finite production rate and imperfect quality under the condition of two-level trade credit policy.
This article develops three inventory models to determine the optimal replenishment policies under permissible delay in payments and shows that the annual total relevant cost functions or profit functions. Associated theorems are established to characterize the optimal solution and obtain the optimal replenishment cycle time and order quantity under various circumstances. Sensitivity analysis is carried out to see how these parameters influence the supply chain model. Finally, illustrated case examples are provided to demonstrate the theoretical results and managerial insights.

參考文獻
1. Aggarwal, S.P. and C.K. Jaggi, 1995. Ordering policies of deteriorating items under permissible delay in payments, Journal of Operational Research Society 46 : 458-662.
2. Buzacott, J.A., 1975. Economic order quantities with inflation, Operational Research Quarterly 26: 553-558
3. Chand, S. and J. Ward, 1987. A note on economic order quantity under conditions of permissible delay in payments, Journal of Operational Research Society 38: 83-84.
4. Chang H.J., C.H. Hung and C.Y. Dye, 2001. An inventory model for deteriorating items with linear trend demand under the condition of permissible delay in payments, Production Planning and Control 12: 274-282.
5. Chang, C.T., 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.
6. Chang, C.T., and J.T. Teng, 2004. Retailer's optimal ordering policy under supplier credits. Mathematical Methods of Operational Research 60: 471-483.
7. Chu, P., K.J. Chung and S.P. Lan, 1998. Economic order quantity of deteriorating items under permissible delay in payments, Computers and Operations Research 25: 817-824.
8. Chung, K.J., 1989. Inventory control and trade credit revisited, Journal of Operational Research Society 40: 495-498.
9. Chung, K.J., 1998. A theorem on the determination of economic order quantity under conditions of permissible delay in payments, Computers and Operations Research 25: 49-52.
10.Chung, K.J., S.K. Goyal, and Y.F. Huang, 2005. The optimal inventory policies under permissible delay in payments depending on the ordering quantity. International Journal of Production Economics, 95: 203–213.
11.Chung, K.J. and T.S. Huang, 2007. The optimal retailer's ordering policies for deteriorating items with limited storage capacity under trade credit financing, International Journal of Production Economics 106: 127-145.
12.Chung, k.J. and C.K. Huang, 2009. An ordering policy with allowable shortage and permissible delay in payments, Applied Mathematical Modelling 33: 2518–2525.
13.Chung, K.J. and C.N. Lin, 2001. Optimal inventory replenishment models for deteriorating items taking account of time discounting, Computers and Operations Research 28: 67-83.
14.Chung, K.J. and J.J. Liao, 2004. Lot-sizing decisions under trade credit depending on the ordering quantity. Computer Operations Research, 31: 909–928.
15.Chung, k.J. and J.J. Liao, 2006. The optimal policy in a discounted cash-flows analysis for deteriorating items when trade credit depends on the order quantity. International Journal of Production Economics 100: 116–130.
16.Chung, K.J. and S.F. Tsai, 2001. Inventory systems for deteriorating items with shortages and a linear trend in demand-taking account of time value, Computers and Operations Research 28: 915-934.
17.Chung, C.T. and S.J. Wu, 2003. A note on 『Optimal payment time under permissible delay in payment for products with deterioration', Production Planning & Control 14: 478-482.
18.Eroglu, A. and G. Oademir, 2007. An economic order quantity model with defective items and shortages, International Journal of Production Economics 106: 544-549.
19.Goyal, S.K., 1985.Economic order quantity under conditions of permissible delay in payments, Journal of Operational Research Society 36: 335-338.
20.Ghare, P.M. and G.F. Schrader, 1963. A model for an exponentially decaying inventory, Journal of Industrial Engineering 14: 238-243.
21.Haley, C.W. and R.C. Higgins, 1973. Inventory policy and trade credit financing, Management Science 20: 464-471.
22.Hariga, M.A., 1995. Effects of inflation and time-value of money on an inventory model with time-dependent demand rate and shortages, European Journal of Operational Research 81: 512-520.
23.Hu,F. and D. Liu, 2010. Optimal replenishment policy for the EPQ model with permissible delay in payments and allowable shortages, Applied Mathematical Modelling 34: 3108-3117.
24.Huang, C.K. 2001. An integrated inventory model for supplier and retailer with defective items, Journal of Information & Optimization Sciences 22(3): 509-519.
25.Huang, C.K., 2002. An integrated vendor-buyer cooperative inventory model for Items with imperfect quality. Production Planning and Control 13: 355-361.
26.Huang, K.N., and J.J. Liao, 2008. A simple method to locate the optimal solution for exponentially deteriorating items under trade credit financing, Computers and Mathematics with Applications 56: 965–977.
27.Huang, Y.F., 2003. Optimal retailer's ordering policies in the EOQ model under trade credit financing, Journal of the Operational Research Society 54: 1011-1015.
28.Huang, Y.F., 2007. Optimal retailer's replenishment decisions in the EPQ model under two levels of trade credit policy, European Journal of Operational Research 176: 1577-1591.
29.Huang, Y.F., and K.J. Chung, 2003. Optimal replenishment and payment polices in the EOQ model under cash discount and trade credit. Asia-Pacific Journal of Operational Research 20: 177-190.
30.Huang, Y.F., and K.H. Hsu, 2008. An EOQ model under retailer partial trade credit policy in supply chain, International Journal of Production Economic 112: 655-664.
31.Huang, Y.F. and Y.S. Lin, 2005. An EPQ model under permissible delay in payments and cash discount. Journal of Applied Sciences 5(2): 273-276.
32.Hwang, H. and S.W. Shinn, 1997. Retailer's pricing and lot sizing policy for exponentially deteriorating products under the condition of permissible delay in payments, Computers and Operations Research 24: 539-547.
33.Jaggi, C.K., S.K. Goyal, and, S.K. Goel, 2008. Retailer's optimal replenishment decisions with credit-linked demand under permissible delay in payments, European Journal of Operational Research 190: 130-135.
34.Jamal A.M.M., 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.
35.Kim, C.H. and Y. Hong, 1999. An optimal production run length in deteriorating production processes, International Journal of Production Economic 58: 183–189.
36.Liao, J.J., 2007. On an EPQ model for deteriorating items under permissible delay in payments, Applied Mathematical Modelling 31: 393-403.
37.Liao, J.J., 2008. An EOQ model with noninstantaneous receipt and exponentially deteriorating items under two-level trade credit, International Journal of Production Economic 113: 852–861
38.Liao, H.C., C.H. Tsai and C.T. Su, 2000. An inventory model with deteriorating items under inflation when a delay in payment is permissible, International Journal of Production Economics 63: 207-214.
39.Ouyang, L.Y. and H.C. Chang, 2002. Lot size reorder point inventory model with
controllable lead time and set-up cost, International Journal of Systems Science 33:635-642.
40.Ouyang, L.Y. and H.C. Chang, 2000. Impact of investing in quality improvement on(Q,r,L) model involving the imperfect production process, Production Planning ＆Control, 11(6): 598-607.
41.Ouyang, L.Y., C.T. Chang, and J.T. Teng, 2005. An EOQ model for deteriorating items under trade credits, Journal of the Operational Research Society 56: 719–726.
42.Ouyang, L.Y., M.S. Chen, and K.W. Chung, 2002. Economic order quantity modelunder cash discount and payment delay, International Journal of Information and Management Sciences 13: 1-10
43.Papachristos, S., and I. Konstantaras, 2006. Economic ordering quantity models for items with imperfect quality. International Journal of Production Economics 100: 148-154.
44.Porteus, E.L. 1986. Optimal lot sizing, process quality improvement and setup cost reduction, Operations Research 34: 137-144.
45.Rosenblatt, M.J., and H.L. Lee, 1986. Economic production cycles with imperfect production processes, IEE Transactions 18: 48-55.
46.Thangam, A.,and R. Uthayakumar, 2009. Two-echelon trade credit financing for perishable items in a supply chain when demand depends on both selling price and credit period, Computers & Industrial Engineering 57 : 773-786.
47.Shah, N.H., 1993. A lot-size model for exponentially decaying inventory when delay in payments is permissible, Cahiers du CERO 35 : 115-123.
48.Salameh, M.K., and M.Y.Jaber, 2000. Economic production quantity model for items with imperfect quality, International Journal of Production Economics 64: 59-64.
49.Sana, S. and K.S. Chaudhuri, 2008. A deterministic EOQ model with delays in payments and price-discount offers, European Journal of Operational Research 184: 509-533.
50.Sarker, B.R., A.M.M. Jamal and S. Wang, 2000. Supply chain models for perishable products under inflation and permissible delay in payment, Computers and Operations Research 27: 59-75.
51.Schwaller, R.L. 1988. EOQ under inspection costs, Production and Inventory Management Journa 29: 22-24.
52.Shawky A.I. and M.O. Abou-El-Ata, 2001. Constrained production lot-size model with trade-credit policy: 』a comparison geometric programming approach via Lagrange, Production Planning and Control 12: 654-659.
53.Shinn, S.W. and H. Hwang, 2003, Optimal pricing and ordering policies for retailer sunder order-size-dependent delay in payments, Computers and Operations Research 30: 35-50.
54.Wee, H.M. and S.T. Law, 2001. Replenishment and pricing policy for deteriorating items taking into account the time-value of money, International Journal of Production Economics 71: 213-220.