A note on integrated single vendor single buyer model with stochastic demand and variable lead time

Ben-Daya and Hariga [2004. Integrated single vendor single buyer model with stochastic demand and variable lead time. International Journal of Production Economics 92, 75-80] recently proposed the paper about integrated single vendor single buyer model with stochastic demand and variable lead time. The lead time is proportional to the lot size produced by the vendor in addition to a fixed delay due to the transportation, setup and nonproductive time. The end-customers accept backorders when the shortage occurs at the buyer side. An order to the vendor is placed each time the inventory level reaches the reorder point. In this note, a modified model is proposed under a different assumption that there are two different reorder points and service levels.