Multi-Echelon Inventory Management Under Short-Term Take-or-Pay Contracts

We extend the Clark-Scarf serial multi-echelon inventory model to include procuring production inputs under short-term take-or-pay contracts at one or more stages. In each period, each such stage has the option to order/process at two different cost rates; the cheaper rate applies to units up to the contract quantity selected in the previous period. We prove that in each period and at each such stage, there are three base-stock levels that characterize an optimal policy, two for the inventory policy and one for the contract quantity selection policy. The optimal cost function is additively separable in its state variables, leading to conquering the curse of dimensionality and the opportunity to manage the supply chain using independently acting managers. We develop conditions under which myopic policies are optimal and illustrate the results using numerical examples. We establish and use a generic one-period result, which generalizes an important such result in the literature. Extensions to cover variants of take-or-pay contracts are included. Limitations are discussed.