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# Ordering Cost Depletion in Inventory Policy with Imperfect Products and Backorder Rebate

Sandeep Kumar1, Teekam Singh1,2, Kamaleldin Abodayeh3, Wasfi Shatanawi3,4,5,*

1 Department of Mathematics, Graphic Era Hill University, Dehradun, 248002, India
2 Department of Mathematics, Graphic Era Deemed University, Dehradun, 248002, India
3 Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
4 China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan
5 Department of Mathematics, Hashemite University, Zarqa, 13133, Jordan

* Corresponding Author: Wasfi Shatanawi. Email:

Computers, Materials & Continua 2021, 66(3), 2343-2357. https://doi.org/10.32604/cmc.2021.014224

## Abstract

This study presents an inventory model for imperfect products with depletion in ordering costs and constant lead time where the price discount in the backorder is permitted. The imperfect products are refused or modified or if they reached to the customer, returned and thus some extra costs are experienced. Lately some of the researchers explicitly present on the significant association between size of lot and quality imperfection. In practical situations, the unsatisfied demands increase the period of lead time and decrease the backorders. To control customers' problems and losses, the supplier provides a price discount in backorders during shortages. Also, an order’s policies may result in including some imperfect products in arrival lots. A discount on price may be offered by the supplier on the out-of-stock products to manage the backorder problems. The study aims to develop a model with imperfect products by permitting the price discount in backorders, and the cost of ordering is considered a decision variable. First, it is assumed that the demand for lead time is followed by a normal distribution and then stops it and assumed that the first two moments of demand for lead time are known. Further, the minimax distribution method is used to solve this model, and a separate algorithm is designed. In this study, two models are discussed with and without a normally distributed rate of demand. The current study verified with the help of some numerical examples over various model parameters.

## Keywords

S. Kumar, T. Singh, K. Abodayeh and W. Shatanawi, "Ordering cost depletion in inventory policy with imperfect products and backorder rebate," Computers, Materials & Continua, vol. 66, no.3, pp. 2343–2357, 2021.

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