Dynamic replenishment from two sources with different yields, costs, and leadtimes

We study a single-item periodic-review inventory system with two sources of supply: in-house production and outsourcing. The two sources differ in yields, costs, and leadtimes. Demands in consecutive periods are independent random variables and stockout is fully backlogged. Our problem is to characterize the optimal dynamic policy that simultaneously determines the in-house production quantity and the outsourcing quantity for each period to minimize the total discounted cost. We show that the optimal policy for in-house production can be characterized by a threshold and the production quantity is decreasing in the starting inventory. The optimal outsourcing policy, however, is more complex, and a threshold-type policy is only optimal under a more restrictive assumption about the yields. Comparative statics about the effects of yield uncertainty, outsourcing on the optimal policy, and cost performance are discussed.