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研究生:鄭家祐
研究生(外文):Cheng Chia-Yu
論文名稱:在延遲付款與現金折扣條件下的經濟生產批量模式之最佳補貨與付款策略
論文名稱(外文):The Optimal Replenishment and Payment Policy for EPQ Models under Conditions of Permissible Delay in Payments and Cash Discount
指導教授:林仁彥
指導教授(外文):Lin Jen-Yen
學位類別:碩士
校院名稱:國立嘉義大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
畢業學年度:100
語文別:中文
中文關鍵詞:經濟生產批量現金折扣延遲付款
外文關鍵詞:EPQcash discountpermissible delay in payments
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供應商為吸引更多零售商向其訂貨,供應商可提供延遲付款策略吸引零售商,即零售商可在付款期限之前先將累積的營收進行投資賺取利潤。然而對於供應商來希望儘早拿到貨款,故供應商亦可提供現金折扣策略,即零售商在付款期限內繳交的貨款,都能享有一定的折扣,藉此來鼓勵零售商提早繳交貨款。因此在本研究中,我們探討同時在延遲付款與現金折扣兩個條件下,單階段付款與二階段付款的經濟批量模型最佳化補貨及付款策略。並對於這兩種情境建立經濟生產批量模型及推導理論分析,提出最佳化求解演算法,協助零售商可擬定最佳的補貨時間與付款策略。
1 序論.....................................................1
1.1 研究動機與背景...........................................1
1.2 研究目的................................................2
1.3 研究流程................................................2
2 文獻回顧..................................................4
2.1 在延遲付款條件下之 EPQ 模型的相關研究.......................5
2.2 在延遲付款與現金折扣條件下之 EPQ 模型的相關研究...............6
3 在延遲付款與現金折扣條件下的經濟生產批量模型之最佳補貨與付款策略....11
3.1 建立數學模型............................................11
3.2 二階段付款策略的模型建立..................................13
3.3 平均總成本函數..........................................19
3.4 平均總成本函數的理論結果..................................27
3.5 演算法................................................34
4 數值實驗結果與未來研究.....................................43
4.1 數值實驗...............................................43
4.2 敏感度分析.............................................44
4.3 未來研究...............................................48
5 參考文獻.................................................50
A 附錄....................................................53
A.1 二階段付款策略的模型建立..................................53
A.2 平均總成本函數的性質證明..................................63
A.3 平均總成本函數的理論結果證明...............................94
A.4 實驗數據表格...........................................116
[1] F. W. Harris. How many parts to make at once. Operations Research, 38(6):947–950,
1990.
[2] S. K. Goyal. Economic order quantity under conditions of permissible delay in payments.
The Journal of the Operational Research Society, 36(4):335–338, 1985.
[3] Ouyang L.-Y., Chen M.-S., and Chuang K.-W. Economic order quantity model under
cash discount and payment delay. Information and management Sciences, 13(1):1–10,
2002.
[4] Chung K.-J. and Huang Y.-F. The Optimal Cycle Time for EPQ Inventory Model
under Permissible Delay in Payments. International Journal of Production Economics,
84(3):307–318, 2003.
[5] Huang Y.-F. and Lin Y.-S. An EPQ Model under Permissible Delay in Payments and
Cash Discount. Journal of Applied Sciences, 5:273–276, 2005.
[6] Huang Y.-F. and Chung K.-J. Optimal Replenishment and Payment Policies in the EOQ
Model Under Cash Discount and Trade Credit. Asia-Pacific Journal of Operational
Research, 20:177–190, 2003.
[7] Huang Y.-F. and Hsu K.-H. EPQ Models under Permissible Payment Delay: An Alge-
braic Approach. Journal of Applied Sciences, 7:515–518, 2007.
46

[8] Ouyang L.-Y., Chuang K.-W., and Chuang B.-R. An Inventory Model with Noninstan-
taneous Receipt and Permissible Delay in Payments. International Journal of Informa-
tion and Management Sciences, 15(3):1–11, 2004.
[9] Huang Y.-F. and Lai C.-S. Extended the EPQ Inventory Model under Permissible Delay
in Payments. Journal of Engineering and Applied Sciences, 2:149–156, 2007.
[10] Teng J.-T. On the economic order quantity under conditions of permissible delay in
payments. Journal of the Operational Research Society, 53(8):915–918, 2002.
[11] Huang Y.-F. and Huang H.-F. Optimal Inventory Replenishment Policy for the EPQ
Model under Trade Credit Derived without Derivatives. International Journal of Sys-
tems Science, 39(5):539–546, 2008.
[12] Huang Y.-F. Optimal Retailer’s Replenishment Decisions in the EPQ Model under Two
Levels of Trade Credit Policy. European Journal of Operational Research, 176(3):1577–
1591, 2007.
[13] Huang Y.-F., Chou C.-L., and Liao J.-J. An EPQ Model under Cash Discount and
Permissible Delay in Payments Derived without Derivatives. Yugoslav Journal of Op-
erations Research, 17(2):177–193, 2007

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