The majority of the researches in the integrated vendor-buyer inventory problem assume that the shipments are equal. In this paper, shipments are considered to be non-equal. Both demand and delivery times are also assumed to be stochastic. Moreover, unsatisfied demand can be backordered and lost, as well asconsidering a service level constraint. The objective is to minimize both buyer and vendor costs at the same time. The problem is solved by an exact heuristic algorithm. To validate the algorithm’s performance, the results are compared with that of LINGO solver. Finally, a set of numerical problems is applied to compare the result in the integrated and independent forms.