Stationary Distribution and Perturbation Bounds for a Stochastic Inventory Model

In this paper, we use the theory of generalized inverses to compute the stationary distribution of the ( s, S ) inventory model directly from the transition matrix of the underlying Markov chain and to provide perturbation bounds. Indeed, approximations are employed to build a tractable model, and s...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 237; no. 5; pp. 722 - 729
Main Author Rabta, B.
Format Journal Article
LanguageEnglish
Published New York Springer US 21.03.2019
Springer
Springer Nature B.V
Subjects
Analysis
Approximation
APPROXIMATIONS
DISTRIBUTION
Inventory control
Inventory management
Markov analysis
Markov chains
MARKOV PROCESS
Markov processes
MATHEMATICAL METHODS AND COMPUTING
Mathematics
Mathematics and Statistics
MATRICES
Parameter estimation
Perturbation methods
PERTURBATION THEORY
Statistical methods
Stochastic models
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Summary:In this paper, we use the theory of generalized inverses to compute the stationary distribution of the ( s, S ) inventory model directly from the transition matrix of the underlying Markov chain and to provide perturbation bounds. Indeed, approximations are employed to build a tractable model, and statistical methods are used to estimate the unknown parameters and distributions. Hence, the system is subject to perturbations that may cause deviation in the characteristics. The proposed perturbation bound provides a means to estimate the impact of the perturbations on the performance measures of the considered inventory system.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04198-w