We investigate the stochastic integrated inventory model wherein the buyer’s lead time demand follows the mixture of normal distributions. Due to the high acquisition cost of land, we assume that buyer’s maximum permissible storage space is limited and therefore adds a space constraint to the respective inventory system. Besides, it is assumed that the manufacturing process is imperfect and produces defective units, and hence each lot received by the buyer contains percentage defectives. The paper also considers controllable lead time components and ordering cost for the system. Based on lead-time components, a multilevel reorder strategy-based supply chain model is developed for the proposed system, and a Lagrange multiplier method is applied to solve the problem to reduce the expected inventory cost of both buyer and vendor. We develop a solution procedure to find the optimal values and show the applicability of the model and solution procedure in numerical examples.