Integrated single vendor single buyer model with stochastic demand and variable lead time

In this paper, we consider the single vendor single buyer integrated production inventory problem. We relax the assumption of deterministic demand and assume that the lead time is varying linearly with the lot size. The lead time is composed of a lot size-dependent run time and constant delay times such as moving, waiting and setup times. A solution procedure is suggested for solving the proposed model and numerical examples are used to illustrate the benefit of integration. A sensitivity analysis is also performed to explore the effect of key parameters on lot size, reorder point, and expected total cost.