Optimal sales to users who hold inventory

This paper solves the optimal inventory policy when both the supplier and the users can hold inventory: The supplier can hold the good until such a time as a buyer wishes to purchase it; a user can purchase a good before he needs it and hold it until the need arises, or delay the purchase and incur a shortage. The welfare-maximizing policy is shown to require periods of shortage in which no sales are made. We also show that the profit-maximizing policy will involve shorter periods of no-sales than does the welfare-maximizing policy.