Optimal Commodity Trading with a Capacitated Storage Asset

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Abstract
This paper considers the so-called warehouse problem with both space and injection/withdrawal capacity limits. This is a foundational problem in the merchant management of assets for the storage of commodities, such as energy sources and natural resources. When the commodity spot price evolves according to an exogenous Markov process, this work shows that the optimal inventory-trading policy of a risk-neutral merchant is characterized by two stage and spot-price dependent basestock targets. Under some assumptions, these targets are monotone in the spot price and partition the available inventory and spot-price space in each stage into three regions, where it is, respectively, optimal to buy and inject, do nothing, and withdraw and sell. In some cases of practical importance, one can easily compute the optimal basestock targets. The structure of the optimal policy is nontrivial because in each stage the merchant's qualification of high (selling) and low (buying) commodity prices in general depends on the merchant's inventory availability. This is a consequence of the interplay between the capacity and space limits of the storage asset and brings to light the nontrivial nature of the interface between trading and operations. A computational analysis based on natural gas data shows that mismanaging this interface can yield significant value losses. Moreover, adapting the merchant's optimal trading policy to the spot-price stochastic evolution has substantial value. This value can be almost entirely generated by reacting to the unfolding of price uncertainty, that is, by sequentially reoptimizing a model that ignores this source of uncertainty.

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