Optimal Inventory Policies When Sales Are Discretionary
Inventory models customarily assume that demand is fully satisﬁed if suﬀicient stock is available. We analyze the form of the optimal inventory policy if the inventory manager can choose to meet a fraction of the demand. Under classical conditions we show that the optimal policy is again of the ( S,s ) form. The analysis makes use of a novel property of K-concave functions.
Scarf, Herbert E., "Optimal Inventory Policies When Sales Are Discretionary" (2000). Cowles Foundation Discussion Papers. 1521.