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October  2009, 5(4): 867-880. doi: 10.3934/jimo.2009.5.867

## A replenishment policy with defective products, backlog and delay of payments

 1 School of Economics and Management, Southwest Jiaotong University, Chengdu, Sichuan 610031, China, China, China

Received  March 2009 Revised  July 2009 Published  August 2009

This paper develops a model to determine an optimal replenishment policy with defective items and shortage backlogging under conditions of permissible delay of payments. It is assumed that 100% of each lot are screened to separate good and defective items which are classified as imperfect quality and scrap items. Difference between unit selling price and unit purchase cost is also included in our mathematical model and analysis. Under this assumption, we model the retailer's inventory system as an expected profit maximization problem to determine the retailer's optimal inventory cycle time and optimal order quantity. Then, a theorem is established to describe the optimal replenishment policy for the retailer. Finally, numerical examples are given to illustrate the theorem and obtain some managerial phenomena.
Citation: Jun Li, Hairong Feng, Mingchao Wang. A replenishment policy with defective products, backlog and delay of payments. Journal of Industrial & Management Optimization, 2009, 5 (4) : 867-880. doi: 10.3934/jimo.2009.5.867
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