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

A Complete Algebraic Solution to the Optimal Dynamic Rationing Policy in the Stock-Rationing Queue with Two Demand Classes