Dynamic Inventory Management with Total Minimum Order Commitments and Two Supply Options

We study optimal policies for dual-supply inventory systems where a firm commits to buying a total minimum quantity from both supplies or two separate total minimum quantities from each supply over a finite planning horizon. The two supply options differ in their costs and lead times. For the system under the joint commitment, the optimal policy has a simple structure and can be fully characterized by three critical numbers in each period. For the system under the separate commitments, we show that the optimal order quantities in each period are monotonic in the starting inventory and the remaining commitments with bounded sensitivity. Moreover, we establish convergence results on the optimal order quantities when the committed quantity from either supply approaches infinity. These findings highlight the effects of order commitments on the optimal inventory policies. On the basis of these results, we develop a simple heuristic for the system under separate commitments and show numerically that it performs very well. The numerical study further shows that the firm could incur a considerable loss if it ignores or overemphasizes the order commitments when managing its inventory. Finally, we conduct numerical analysis to derive insights into the firm's supply contract selection in the presence of minimum order commitments.