Theory for optimizing capacitated commodity storage with case studies in natural gas

We develop theoretical concepts of optimal injecting and withdrawing for a capacitated commodity storage and give case studies in natural gas. We start with the concept of spot price thresholds, which represent the expected value of future opportunities forgone or created by currently injecting or withdrawing any commodity. Comparison of the spot price with the spot price thresholds dictates when current trading is optimal. Under certain conditions these thresholds decrease monotonically in inventory level, and thus they relate to and extend previous work under a similar setup to ours. That work proves the existence of two critical inventory levels such that injecting, withdrawing or doing nothing, respectively, is optimal for current inventories less than, greater than or between those levels, all else being equal. We find that the current spot price in relation to the thresholds both causes these results and can be used to calculate the critical inventory levels. Also, the gap between the two critical inventory levels is driven mainly by transaction costs.