In this paper, we investigate the supply chain model for a vendor-buyer inventory
problem. We assume that an arrival order lot contains some defective items, and the
defective rate is a random variable. Also, shortages are allowed and the length of lead time
is controllable and reducible by adding additional crashing cost. We derive an integrated
mixture inventory model with backorders and lost sales, in which the order quantity,
reorder point, lead time and the number of shipment from vendor to buyer are decision
variables. Iterative procedure was developed to obtain the optimal production and
replenishment strategy. Furthermore, the effects of parameter are also discussed.
