Lot‐sizing policies for deterioration items under two‐level trade credit with partial trade credit to credit‐risk retailer and limited storage capacity

Abstract

The main purpose of this article is to investigate the optimal wholesaler's replenishment decisions for deterioration items under two levels of the trade credit policy and two storage facilities in order to reflect the supply chain management situation within the economic order quantity framework. In this study, each of the following assumptions have been made: (1) The own warehouse with limited capacity always is not sufficient to store the order quantity, so that a rented warehouse is needed to store the excess units over the capacity of the own warehouse; (2) The wholesaler always obtains the partial trade credit, which is independent of the order quantity offered by the supplier, but the wholesaler offers the full trade credit to the retailer; (3) The wholesaler must take a loan to pay his or her supplier the partial payment immediately when the order is received and then pay off the loan with the entire revenue. Under these three conditions, the wholesaler can obtain the least costs. Furthermore, this study models the wholesaler's optimal replenishment decisions under the aforementioned conditions in the supply chain management. Two theorems are developed to efficiently determine the optimal replenishment decisions for the wholesaler. Finally, numerical examples are given to illustrate the theorems that are proven in this study, and the sensitivity analysis with respect to the major parameters in this study is performed. Copyright © 2016 John Wiley & Sons, Ltd.

Retailer's optimal ordering policy in the EOQ model with imperfect‐quality items under limited storage capacity and permissible delay

“…This would lead to a worthwhile contribution in the supply chain management system. We choose also to refer the interested reader to such related recent developments in the subject as those by Chung et al 15 , to their other recent works, 16,[40][41][42][43][44][45] and by Liao et al 17,18 ).…”

“…Many additional related developments can be found in the works by Sett et al, Yen et al, Yang and Chang, Zhong and Zhou, Soni, Liao et al, Bhunia et al, and the references cited in each of these works. The interested reader is referred also to such related recent works as those by Chung et al to their other recent work) and by Liao et al…”

“…Many additional related developments can be found in the works by Sett et al, 8 Yen et al, 9 Yang and Chang, 10 Zhong and Zhou, 11 Soni, 12 Liao et al, 13 Bhunia et al, 14 and the references cited in each of these works. The interested reader is referred also to such related recent works as those by Chung et al 15 to their other recent work 16 ) and by Liao et al 17,18 On the other hand, in most realistic environment, it can be observed that such situations as (for example) weak process control, deficient planned maintenance, and inadequate work instructions or damage in transit can cause many arriving order lots to contain defective items, which affect the on-hand inventory level, the frequency of orders, and incur additional cost. Furthermore, the inspection of the lot becomes indispensable in all public and private sector organizations.…”

“…2873 8468.5(16) I e = 0.40 ≥ 0 ≥ 0 < 0 T * 2 = 0.2092 8311.4(17) I e = 0.80 ≥ 0 ≥ 0 < 0 T * 2 = 0.2094 8371.7(18) I e = 0.120 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 8432.2 (19) I p = 0.150 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 8432.2 (20) I p = 0.180 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 8387.2 (21) I p = 0.210 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 8342.2 (22) M = 0.10 ≥ 0 ≥ 0 ≥ 0 T * 3 = 0.2091 8447.0 (23) M = 0.150 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 8432.2 (24) M = 0.20 < 0 ≥ 0 < 0 T * 1 = 0.1722 8430.0 (25) d = 0.50 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 8432.2 (26) d = 1.00 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 7876.7 (27) d = 1.50 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 7321.1 (28) c = 0.10 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 8432.2 (29) c = 0.50 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 7987.8 (30) c = 0.90 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 7543.3 (31) r = 0.10 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 8432.2 (32) r = 0.30 < 0 < 0 < 0 T * 1 = 0.1007 7403.4 (33) r = 0.50 < 0 < 0 < 0 T * 1 = 0.0627 5752.6 (34) x = 100 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 8432.2 (35) x = 150 ≥ 0 ≥ 0 < 0 T * 2 = 0.2495 8563.8 (36) x = 200 ≥ 0 ≥ 0 < 0 T * 2 = 0.2827 8643.7 (37) h w = 0.30 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 8432.2 (38) h w = 0.50 ≥ 0 ≥ 0 < 0 T * 2 = 0.2140 8400.6 (39) h w = 0.70 ≥ 0 ≥ 0 < 0 T * 2 = 0.2183 8369.4 (40) h r = 0.20 ≥ 0 ≥ 0 < 0 T * 2 = 0.2096 8432.2 (41) h r = 0.250 ≥ 0 ≥ 0 < 0 T * 2 = 0.1886 8356.0 (42) h r = 0.300 < 0 ≥ 0 < 0 T * 2 = 0.1731 8290.7…”

Some modified mathematical analytic derivations of the annual total relevant cost of the inventory model with two levels of trade credit in the supply chain system

“…In their recent works, many researchers started to consider such other factors as (for example) trade credit, which means that, during the permissible delay period, the retailer can sell the item and generate the revenue and incur interest on it by depositing in the bank or financial firms. (See the recent works on this subject by, for example, Chung et al, [1][2][3] Liao et al, [4][5][6] Srivastava et al, 7 and by others; see also the references that are cited in each of these earlier works).…”