# American Institute of Mathematical Sciences

October  2016, 12(4): 1333-1347. doi: 10.3934/jimo.2016.12.1333

## An inventory model for items with imperfect quality and quantity discounts under adjusted screening rate and earned interest

 1 Department of Marketing and Supply Chain Management, Overseas Chinese University, Taichung 40721, Taiwan 2 Department of Business Administration, National Chung Cheng University, Chia-Yi 621, Taiwan 3 Department of Industrial Engineering and Management, Overseas Chinese University, Taichung 40721, Taiwan

Received  October 2014 Revised  October 2015 Published  January 2016

In this paper we develop a new inventory model for items with imperfect quality and quantity discounts under adjusted screening rate and earned interest. Three highlights are included in this new model: (1) interest is earned by depositing the sales revenue from the perfect and imperfect items into an interest-bearing account (2) the screening rate may not be given but is a decision variable (3) the supplier offers quantity discounts to trigger the retailer into ordering greater lot sizes. This scenario has not been discussed in previous EOQ models with imperfect quality. Our model could determine two decision variables, order quantity and screening rate, to maximize retailer profit. The expected total profit function is derived with two special cases explored to validate the proposed model. An algorithm is developed to help the manager determine the optimal order quantity and screening rate. A numerical example is given to illustrate the proposed model and algorithm. Sensitivity analyses are carried out to investigate the model parameters effects on the optimal solution. Managerial insights are also included.
Citation: Tien-Yu Lin, Ming-Te Chen, Kuo-Lung Hou. An inventory model for items with imperfect quality and quantity discounts under adjusted screening rate and earned interest. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1333-1347. doi: 10.3934/jimo.2016.12.1333
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