Many natural resources and energy sources are commodities. According to the Webster’s New Universal Unabridged Dictionary (1996 [43]), a commodity is “any unprocessed or partially processed good, as grains, fruits, and vegetables, or precious metals.” Coal, oil, and natural gas are additional examples. For a storable commodity, the economic interpretation of storage is the amount of commodity carried over to the next period from the current period; that is, storage from the prior period plus the difference between the commodity production and consumption in the current period (Williams and Wright 1991 [45]). Professional commodity storers, hereafter referred to as merchants, trade this surplus in wholesale markets that, for basic commodities, resemble a situation of perfect competition; that is, they are characterized by many small players who behave as price takers. For example, such a setting is the natural gas market at Henry Hub, Louisiana, the delivery location of the New York Mercantile Exchange (NYMEX) natural gas futures contract.
Merchants need access to storage facilities to support their commodity trading activities. They may own such facilities themselves, or hold contracts on their capacity. In this paper, a storage asset refers to the facility where a commodity can be physically stored, or a contractual agreement that entitles its owner to usage of a portion of such a facility. These assets feature two distinctive characteristics. On the operational side, while the storage technology may take many forms (from conventional warehouses and oil tanks to underground depleted reservoirs, aquifers, and salt domes used to store natural gas), minimum/maximum inventory levels (space) and injection/withdrawal capacity limits are ubiquitous. On the financial side, commodity prices are notoriously variable and volatile (Seppi 2002 [34]), and storage assets give their managers (merchants) the real option (Trigeorgis 1996 [40]) to buy the commodity at one point in time, store it, and sell it at a later point in time to exploit price variability and volatility.
Focus. This paper focuses on the commercial management of a commodity storage asset. This requires determining an inventory trading policy that, given the current commodity spot price and inventory available in the storage facility, tells the merchant how much commodity to buy from the wholesale market and inject into this facility, or withdraw from this facility and sell into the wholesale market. This is a foundational problem in the commercial management of commodities, which has been studied in the literature on the warehouse problem. Cahn (1948 [5]) introduces this problem as follows: “Given a warehouse with fixed capacity and an initial stock of a certain product, which is subject to known seasonal price and cost variations, what is the optimal pattern of purchasing (or production), storage and sales?” The fixed capacity attribute here refers to a finite size warehouse without restrictions on how fast it can be filled up or emptied. As will become apparent below, this qualification is critical. Charnes and Cooper (1955 [6]) discuss network flow formulations of this problem. Bellman (1956 [1]) presents a dynamic programming formulation, and Dreyfus (1957 [9]) shows that its optimal policy is simple: in each stage, given the current price, if it is optimal to trade then empty/fill-up the facility, and do nothing otherwise. This is a simple type of critical level, or, equivalently, basestock inventory trading policy. Charnes et al. (1966 [7]) extend this work to include stochastic prices and show that this property persists in this case.
Download
Optimal Commodity Trading with a Capacitated Storage Asset
