COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1270

Optimal Inventory Policies When Sales Are Discretionary

Herbert E. Scarf

August 2000

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.

Keywords: Inventory theory, optimal ordering policies, (S,s) policies, K-concavity

JEL Classification: C6