Production control in the face of storable raw material, random supply, and an outside market

We study a periodic-review production/inventory control problem where both the supply of raw material and demand for the finished product are exogenous and random, the raw material can be stored for future use, can be purchased from or sold to an outside market. We study both the lost sales and backlogging cases under both strict convex and linear raw material purchasing/selling costs. Convexity of the purchasing/selling cost implies that the more the firm purchases from or sells to the outside market, the more expensive or less valuable the raw material becomes. For all cases, we find the partial characterizations for the optimal policies, which all turn out to be very intuitively appealing. In particular, for each of the linear-cost cases, the optimal policy degenerates into a combination of two base-stock policies: one for the raw material inventory and the other for the finished product inventory.