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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

An integrated supply chain inventory model with imperfect-quality items, controllable lead time and distribution-free demand