Improved quality, setup cost reduction, and variable backorder costs in an imperfect production process

This paper illustrates the relationship between quality improvement, reorder point, and lead time, as affected by backorder rate, in an imperfect production process. To reduce the total system cost by optimizing the setup cost, lot size, lead time, reorder point, and process quality parameter simultaneously, we first consider that the lead time demand follows a normal distribution, then we apply the distribution free approach for the lead time demand. We prove two lemmas which are used to find optimal solutions for the basic and distribution free models. We compare our models with the existing models using numerical examples and show that significant savings over the existing models can be achieved.