We consider a seller who wishes to sell K goods by time T. Potential buyers enter IIDover time and are patient. At any point in time, profit is maximized by awarding the goodto the agent with the highest valuation exceeding a cutoffs. These cutoffs are characterizedby a one-period-look-ahead rule and are deterministic, depending only on the number ofunits left and the time remaining. The cutoffs decrease over time and in the inventory size,with the hazard rate of sales increasing as the deadline approaches. In the continuous timelimit, the optimal allocation can be implemented by posted-prices with an auction at timeT. Unlike the cutoffs, the prices depend on the history of past sales.