We consider a firm facing random demand at the end of a single period of random length. At any time during the period, the firm can either increase or decrease inventory by buying or selling on a spot market where price fluctuates randomly over time, and the revenue the firm gets by meeting demand at the end of the period is a function of the spot market price at that time. We first demonstrate that this control problem is equivalent to a singular control problem of higher dimensions. We then use this insight combined with a novel control-theoretic approach to show that the optimal policy is completely characterized by a simple price-dependent two threshold policy. In a series of computational experiments, we explore the value of actively managing inventory during the period rather than making a purchase decision at the start of the period, and then waiting for demand.
October 6, 2007
2007 Working Papers