Inventory flexibility through adjustment contracts

We study the problem of inventory management for a buyer whose ordering is governed by a multi-period adjustment contract that allows the buyer to adjust his inventory level upwards or downwards during an ordering period. Under this type of arrangement, the buyer has added flexibility in inventory control so as to reduce his inventory risk. This flexibility, however, comes at a cost, i.e. at a higher price per unit of inventory bought and a lower price per unit of inventory sold during an ordering period. A supply contract of this type provides the additional ordering flexibility buyers often demand, while allowing the supplier to charge for the additional cost associated with this flexibility. We prove the structure of the optimal inventory policy for a buyer who procures inventory under a portfolio of supply contracts, consisting of a wholesale price contract and an adjustment contract. We then extend our analysis to consider positive lead times and fixed order costs. Finally, we quantify the benefits of using the adjustment contract for the buyer.