Integrated vendor–buyer supply chain model with vendor’s setup cost reduction

This paper deals with an integrated vendor–buyer supply chain model. Two models are constructed based on the probability distribution of the lead time demand. The lead time demand follows a normal distribution in the first model. In the second model, we consider the distribution free approach for the lead time demand. For the second model, only mean and standard deviation are known. The aim of our model is to reduce the total system cost by considering the setup cost reduction of the vendor. Finally, some numerical examples are presented to illustrate the models.