An inventory model for deteriorating items under the condition of permissible delay in payments

Abstract

In economic order quantity (EOQ) models, it is often assumed that the payment of an order is made on the receipt of items by the inventory system. However, such an assumption is not quite practical in the real world. Under most market behaviors, it can be easily found that a vendor provides a credit period for buyers to stimulate demand. In this paper, a varying rate of determination and the condition of permissible delay in payments used in conjunction with the economic order quantity model are the focus of discussion. Numerical examples are presented to illustrate the proposed models

Reviewing the Literature of Inventory Models under Trade Credit Contact

“…They demonstrated theoretical results by an illustrative example and specific graphical results. Moussawi-Haidar et al [162] developed a threeechelon supply chain model, including a supplier, a retailer, and a bank, where the retailer is offered a credit period by the [5] EOQ Co nstan t ------Chapman et al [6] EOQ Co nstan t ------Goyal [7] EOQ Co nstan t ------Ventura [8] E O Q C o n s t a n t --✓ ---Dave [9] EOQ Co nstan t ------Chung [10] EOQ Co nstan t -----✓ Jaggi and Aggarwal [11] E O Q C o n s t a n t -✓ ---✓ Aggarwal and Jaggi [12] E O Q C o n s t a n t -✓ ----Khouja and Mehrez [13] EOQ Co nstan t ---✓ --Hwang and Shinn [14] EOQ Price dependent -✓ ----Jamal et al [15] E O Q C o n s t a n t ✓ ✓ ----Chung [16] EOQ Co nstan t ------Chu et al [17] E O Q C o n s t a n t -✓ ----Sarker et al [18] E O Q C o n s t a n t ✓ ✓ ---✓ Liao et al [19] EOQ Stock dependent -✓ ---✓ Jamal et al [20] E O Q C o n s t a n t -✓ ----Chang and Dye [21] E O Q C o n s t a n t ✓ ✓ ----Chung et al [22] E O Q C o n s t a n t -✓ ----Chang et al [23] E O Q C o n s t a n t -✓ ----Teng [24] EOQ Co nstan t ------Ouyang et al [25] EOQ Co nstan t ------Shinn and Hwang [26] EOQ Price dependent ---✓ --Abad and Jaggi [27] N o ncoo pera tiveandcoo pera tive Pricedependen t ------Chung and Huang [28] EOQ Co nstan t ------Chung and Huang [29] EPQ Co nstan t ------Huang [30] E O Q C o n s t a n t --✓ ---Chang et al [31] EOQ Time dependent -✓ -✓ --Huang and Chung [32] EOQ Co nstan t ------Chung and Liao [33] E O Q C o n s t a n t -✓ -✓ --Chang and Teng [34] E O Q C o n s t a n t -✓ ----Chung et al [35] EOQ Co nstan t ---✓ --Ouyang et al [36] E O Q C o n s t a n t -✓ ----Teng et al…”

“…Considering the same model as Hwang and Shinn [14], Chung et al [22] gave a rigorous proof to the concavity of their proposed model and presented an algorithm to find the optimal cycle time. Having assumed the same selling price and purchasing cost, Chang et al [23] obtained the optimal replenishment time in an EOQ inventory model with two types of deterioration, linear as well as Weibull deterioration rates. Chang and Teng [34] developed Goyal's [7] model to the case of deterioration and cash discount and compared the proposed model with the classical economic order quantity.…”

“…Singh and Sharma [155] generalized Sarkar's [115] model to the case of deterioration and demand-dependent production. Tung et al [158] provided a patch work for Chang et al [23] to assist researchers in absorbing and applying their important findings. Wang et al [159] proposed an EOQ model of a vendor and determined his optimal cycle time and credit period for the products with credit-dependent demand and maximum lifetime.…”

An inventory planning problem for time-varying linear demand and parabolic holding cost with salvage value

“…An inventory control model for economic order quantity of deteriorating items under permissible delay in payments was developed in [5]. As an economic order quantity model, an inventory control system for deteriorating items with time varying demand was formulated in [7], where the partial backlogging is considered. For a single period inventory problem with quadratic demand distribution, an expression for the total cost function was modeled in [3] under the influence of market policies.…”

An EOQ model for a deteriorating item with time dependent quadratic demand and variable deterioration under permissible delay in payment

“…Shinn, Hwang and Sung [24], Chu, Chang and Lan [25], Chung, Chang and Yang [26] also entered Goyal's model for the case of deteriorating items. Other notable works in this direction come from Davis and Gaither [27], Mandal and Phaujder [28], Aggarwal and Jaggi [29], Chang and Dye [30], Salmeh, Abboud, Ei-Kassar and Ghattas [31], Chung and Lio [32], Sana and Chaudhuri [33] etc. Recently, Khanna, Ghosh and Chaudhuri [23] developed an EOQ model for a deteriorating item with quadratic demand rate under permissible delay in payment.…”