An accurate and reliable mathematical analytic solution procedure for the EOQ model with non-instantaneous receipt under
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An accurate and reliable mathematical analytic solution procedure for the EOQ model with non-instantaneous receipt under supplier credits H. M. Srivastava1,2,3 Shih-Fang Lee8
· Kun-Jen Chung4,5 · Jui-Jung Liao6
· Shy-Der Lin7 ·
Received: 21 August 2020 / Accepted: 30 September 2020 © The Royal Academy of Sciences, Madrid 2020
Abstract Recently, Huang and Hsu (J Oper Res Soc Jpn 50:1–13, 2007) investigated the retailer’s optimal replenishment policy with non-instantaneous receipt under trade credit and cash discount. Basically, their inventory model is correct and interesting. However, they ignored explorations of interrelations of functional behaviors of the annual total cost to locate the optimal solutions so much so that the accuracy and reliability of the process of the proof of their solution procedure are questionable. The main purpose of this paper is to provide accurate and reliable mathematical analytic solution procedures to improve the findings in the aforementioned work of Huang and Hsu (J Oper Res Soc Jpn 50:1–13, 2007). Some related recent works on the subject-matter of this investigation are also cited with a view to providing incentive and motivation for making further advances along the lines of the supply chain management and associated inventory problems which we have discussed in this article. Keywords Mathematical analytic solution procedure · Inventory model · Retailer’s optimal replenishment policy · Economic order quantities (EOQ) · Trade credits · Cash discounts · Permissible delay in payment · Cash discount Mathematics Subject Classification Primary 26A06 · 26A24 · 91B24 · 93C15; Secondary 26D10 · 90B30.
1 Introduction In the year 1998, Borde and McCarty [1] pointed out that, in inventory management, economic order quantities (EOQ) may be affected as a result of the payment delays associated with trade credit, which implies that interactions may occur between trade credit and other operational considerations. From a retailer’s viewpoint, not accepting the discount and paying later may be advantageous in the presence of rapid inflation in which case a finite fund would become worthless in real terms. On the other hand, from the supplier’s perspective, Hill and Riener [8] identified several benefits and costs which are associated with cash discounts. Cash discounts
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typically induce some customers to pay early in exchange for a pre-specified discount. To the supplier, cash is received sooner, thereby reducing the need to borrow. An early payment discount is, in effect, a price reduction. If retailers are price elastic, cash discounts may generate greater demand for the firm’s products. Thus, cash discount can be used as a tool in the process of fine tuning the product’s price. Early payment may reduce the possibility of bad debt losses as less time would be available for buyers to develop and resolve the paymentrelated problems. However, on the nega
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