In this paper, we consider an integrated vendor-buyer inventory policy for a continuous review model with a random number of defective items and screening process gradually at a fixed screening rate in buyer’s arriving order lot. We assume that shortages are allowed and partially backlogged on the buyer’s side, and that the lead time demand distribution is unknown, except its first two moments. The objective is to apply the minmax distribution free approach to determine the optimal order quantity, reorder point, lead time and the number of lots delivered in one production run simultaneously so that the expected total system cost is minimized. Numerical experiments along with sensitivity analysis were performed to illustrate the effects of parameters on the decision and the total system cost.