Abstract
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 for the optimal dynamic rationing policy. To do this, we establish a policy-based birth-death process to 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). Crucially, we characterize the monotonicity and optimality of the long-run average profit of this system, and establish some new structural properties of the optimal dynamic rationing policy by observing any given reference policy. Finally, we use numerical examples to verify computability of our theoretical results. We believe that the methodology and results developed in this paper can shed light on the study of stock-rationing queue and open a series of potentially promising research.
Supported by the National Natural Science Foundation of China under grant No. 71932002.
J.-Y. Ma and Q.-L. Li—Contributed to the work equally and should be regarded as co-first authors.
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Li, QL., Li, YM., Ma, JY., Liu, HL. (2022). The Optimal Dynamic Rationing Policy in the Stock-Rationing Queue. In: Ni, Q., Wu, W. (eds) Algorithmic Aspects in Information and Management. AAIM 2022. Lecture Notes in Computer Science, vol 13513. Springer, Cham. https://doi.org/10.1007/978-3-031-16081-3_7
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