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AIMS Mathematics

2023, Volume 8, Issue 8: 19546-19565. doi: 10.3934/math.2023997
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Research article

$ (s, S) $ Inventory policies for stochastic controlled system of Lindley-type with lost-sales

  • Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Av. San Claudio, San Manuel, Ciudad Universitaria, 72570, Puebla, México
  • Received: 21 February 2023 Revised: 05 June 2023 Accepted: 06 June 2023 Published: 09 June 2023

  • MSC : 49J53, 49K99

  • This paper presents a characterization of $ (s, S) $-inventory policies for Lindley systems with possibly unbounded costs, where the objective is to minimize the expected discounted total cost by ordering (production) strategies. Moreover, the existence of a subsequence of minimizers of the value iteration functions that converge to a $ (s, S) $ optimal inventory system policy is shown. A numerical example is given to illustrate the theory.

    Citation: Rubén Blancas-Rivera, Hugo Cruz-Suárez, Gustavo Portillo-Ramírez, Ruy López-Ríos. $ (s, S) $ Inventory policies for stochastic controlled system of Lindley-type with lost-sales[J]. AIMS Mathematics, 2023, 8(8): 19546-19565. doi: 10.3934/math.2023997

    Related Papers:

  • This paper presents a characterization of $ (s, S) $-inventory policies for Lindley systems with possibly unbounded costs, where the objective is to minimize the expected discounted total cost by ordering (production) strategies. Moreover, the existence of a subsequence of minimizers of the value iteration functions that converge to a $ (s, S) $ optimal inventory system policy is shown. A numerical example is given to illustrate the theory.


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