This article presents the single-vendor single-buyer integrated production inventory models. We relax the assumption that lead time demand, X, is deterministic and assume that it is stochastic. Also, we assume that shortage during the lead time is permitted, and lead time can be reduced at an added cost. Two models are considered here. In the first model, the demand of lead time follows a normal distribution, and in the second model, it is distribution-free. For both cases, we develop effective iterative procedures for finding the optimal policy and numerical examples are used to illustrate the benefits of integration.
International Journal of Production Economics 92(3), pp.255-266