The Optimal Cycle Time for EOQ Inventory Model under Permissible Delay in Payments

允許延後付款情況下之EOQ存貨模式的最佳存貨週期

黃勇富(Yung-Fu Huang)

《台灣管理學刊》 1卷1期 (2001/08) Pp. 89-99

https://doi.org/10.6295/TAMJ.2001.0101.06

摘要

1985年Goyal是第一位將允許延後付款條件加入經濟訂購模式中，其假設：(1)品項的單位售價等於單位採購成本。(2)當信用交易期限結束時，零售商需擔負起較高之資金積壓的利息，且當品項一被售出時就馬上還款。
本研究主要修改上述二不符合現實環境的假設。本研究將假設品項的單位售價高於單位採購成本。更進一步，本研究假設零售商在信用交易期限結束時，零售商將向銀行借貸100%貨款以繳交給供應商，而向銀行借貸的款項將於一存貨週期結束時才償還。在此假設下，建構出存貨的數學模式以求出最佳之存貨週期。首先，本研究將證明每年的總變動成本函數為凸函數。在凸函數的性質下，導出一定理，藉此可找出在允許信用交易情況下之最佳存貨週期與訂購量。最後，提出相關數值實例，用以說明此定理。

關鍵字

經濟訂購量 ； 允許延後付款 ； 信用交易 ； 存貨管理

並列摘要

In 1985, Goyal is the first person of considering the economic order quantity under conditions of permissible delay in payments. Goyal assumed that: (1) The unit selling price and the unit purchasing price are equal. (2) At the end of the credit period, the account is settled. The retailer starts paying for higher interest charges on the items in stock and returns money of the remaining balance immediately when the items are sold.
The inventory model developed in this paper analyses the same problem under different assumptions from that of Goyal, reflecting the real life situations. This paper wants to assume that the unit selling price is higher than the unit purchasing price. Furthermore, this paper will propose that at the end of the credit period, the retailers will borrow 100% purchasing cost from the bank to pay off the account and they do not return money to the bank until the end of inventory cycle. Mathematical models have been derived for obtaining the optimal cycle time for items under the conditions of permissible delay in payments. First, this paper shows that the annual total variable cost functions are convex. Second, with convexity, a theorem is developed to determine the global optimal cycle time and the optimal order quantity. Finally, numerical examples are given to illustrate the theorem.

並列關鍵字

EOQ ； Permissible delay in payments ； Trade credit ； Inventory Management