Stochastic Models

Li, Quan-Lin

doi:10.1007/978-3-642-11492-2_1

Cited by 3 publications

(3 citation statements)

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“…If and for any given policy , then the optimal dynamic rationing policy is given by In this case, we obtain and It follows from Subsection 1.1.4 of Chapter 1 in Li ( 2010 ) that At the same time, it follows from ( 8 ) to ( 11 ) that Thus we obtain where …”

Section: Monotonicity and Optimalitymentioning

confidence: 95%

“…In this case, we write the stationary probability vector of the policy-based birth-death process as Obviously, the stationary probability vector is the unique solution to the system of linear equations: and , where is a column vector of ones with a suitable dimension. We write and It follows from Subsection 1.1.4 of Chapter 1 in Li ( 2010 ) that By using the policy-based birth-death process , now we define a more general reward function in the stock-rationing queue. It is seen from Table 1 that the reward function with respect to both states and policies is defined as a profit rate (i.e.…”

Section: Optimization Model Formulationmentioning

confidence: 99%

“…On the other hand, it is worthwhile to note that the RG -factorization of block-structured Markov processes can be extended and generalized to a more general optimal transformational version in the study of stock-rationing block-structured queues. See Li ( 2010 ) and Ma et al. ( 2019 ) for more details.…”

Section: Monotonicity and Optimalitymentioning

confidence: 99%

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A complete algebraic solution to the optimal dynamic rationing policy in the stock-rationing queue with two demand classes

et al. 2023

J Comb Optim

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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 queue and open a series of potentially promising research.

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