A Deterministic Single-Item Inventory Model with Seller Holding Cost and Buyer Holding and Shortage Costs

This paper considers the optimal deterministic inventory policy for a monopolist. The novel element concerns the consumers. Each has a time at which he would most prefer to obtain the good; he incurs a shortage cost if he buys it after that time, and a holding cost if he obtains it before. The firm must consider that any change in its policy will affect the quantity of goods it can sell and the maximum price it can charge. We find that the seller's optimal policy can take only one of three possible forms: sell the goods throughout each cycle; sell the goods continuously during an interval that is shorter than an inventory cycle; or sell the goods only at the instant each cycle begins.