Optimal Inventory-Management-Policy for Commodity Storage-Assets

Commodity storage-assets can be either physical storage-facilities, or contracts guaranteeing their use. Merchants employ them to support their commodity-trading activities in wholesale markets, which are characterized by notoriously volatile prices. Managing a storage asset requires determining an inventory-management policy, which, given a realization of the commodity price, consists of choosing how-much commodity to buy-from, or sell-into, the wholesale market. This policy must simultaneously consider the operational characteristics of the asset and the uncertainty in the commodity price. This paper studies the optimal inventory-management-policy for commodity storage-assets with price-taking merchants and a storage technology characterized by inventory and flow-capability constraints and flow-related commodity-losses. It formulates the problem as a finite-horizon Markov decision process and establishes structural properties of the optimal value-function and inventorymanagement-policy based on a natural characterization of well-behaved flow-capabilities. Given a price realization, the former is increasing and concave in inventory, and the latter has a pricedependent two-sided-basestock-target structure. This work also investigates in more detail the cases of linear and piecewise-linear flow-capability-functions, and, in the latter case, it illustrates its findings with an example.