  In this paper, we study a stock-rationing queue with two demand classes by
means of the sensitivity-based optimization, and develop a complete algebraic
solution to the optimal dynamic rationing policy. We show that the optimal
dynamic rationing policy must be of transformational threshold type. Based on
this finding, we can refine three sufficient conditions under each of which the
optimal dynamic rationing policy is of threshold type (i.e., critical rationing
level). To do this, we use the performance difference equation to characterize
the monotonicity and optimality of the long-run average profit of this system,
and thus establish some new structural properties of the optimal dynamic
rationing policy by observing any given reference policy. Finally, we use
numerical experiments to demonstrate our theoretical results of the optimal
dynamic rationing policy. We believe that the methodology and results developed
in this paper can shed light on the study of stock-rationing queues and open a
series of potentially promising research.
