A total minimum commitment contract is a supply contract under which a firm commits to buying a minimum quantity of a product from its supplier during the contract duration (e.g., one year). Such contracts are widely used in industries, because they provide the buyer with flexibility in terms of...

We study a continuous-review, two-echelon inventory system with one central warehouse, multiple local facilities, and each facility facing random demand. Local facilities replenish their stock from the central warehouse (or distribution center), which in turn places orders at an outside supplier...