In supply chain, there are a variety of different uncertainties including demand, service time, lead time, and so forth. The uncertainty of demand has been commonly studied by researchers or practitioners in the field of supply chain. However, the uncertainty of upstream supply chain has also increased. A problem of uncertainty in the upstream supply chain is the fluctuation of the lead time. The stochastic lead time sometimes causes to happen so called the order crossover which is not the same sequences of the order placed and the order arrived. When the order crossover happens, ordinary inventory policies have difficult to find the optimal inventory solutions. In this research, we investigate the lead time distribution in case of the order crossover and explore the resolutions of the inventory solution with the order crossover.