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Retrial Queuing-Inventory Systems with Delayed Feedback and Instantaneous Damaging of Items

Axioms, 2022-05, Vol.11 (5), p.241 [Tạp chí có phản biện]

2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. ;ISSN: 2075-1680 ;EISSN: 2075-1680 ;DOI: 10.3390/axioms11050241

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  • Nhan đề:
    Retrial Queuing-Inventory Systems with Delayed Feedback and Instantaneous Damaging of Items
  • Tác giả: Melikov, Agassi ; Aliyeva, Sevinj ; Nair, Sajeev S. ; Kumar, B. Krishna
  • Chủ đề: Algorithms ; Customer services ; Customers ; Damage ; destructive customers ; Feedback ; feedback customers ; Inventory management ; inventory system ; Lead time ; Markov chains ; Mathematical analysis ; Mathematical models ; Policies ; primary customers ; Probability ; Probability distribution ; Probability distribution functions ; Queueing ; Queuing ; Random variables ; Replenishment ; retrial customers
  • Là 1 phần của: Axioms, 2022-05, Vol.11 (5), p.241
  • Mô tả: This paper studies a Markov model of a queuing-inventory system with primary, retrial, and feedback customers. Primary customers form a Poisson flow, and if an inventory level is positive upon their arrival, they instantly receive the items. If the inventory level is equal to zero upon arrival of a primary customer, then this customer, according to the Bernoulli scheme, either leaves the system or goes into an infinite buffer to repeat their request in the future. The rate of retrial customers is constant, and if the inventory level is zero upon arrival of a retrial customer, then this customer, according to the Bernoulli scheme, either leaves orbit or remains in orbit to repeat its request in the future. According to the Bernoulli scheme, each served primary or retrial customer either leaves the system or feedbacks into orbit to repeat their request. Destructive customers that form a Poisson flow cause damage to items. Unlike primary, retrial, and feedback customers, destructive customers do not require items, since, upon arrival of such customers, the inventory level instantly decreases by one. The system adopted one of two replenishment policies: (s, Q) or (s, S). In both policies, the lead time is a random variable that has an exponential distribution. It is shown that the mathematical model of the system under study was a two-dimensional Markov chain with an infinite state space. Algorithms for calculating the elements of the generating matrices of the constructed chains were developed, and the ergodicity conditions for both policies were found. To calculate the steady-state probabilities, a matrix-geometric method was used. Formulas were found for calculating the main performance measures of the system. The results of the numerical experiments, including the minimization of the total cost, are demonstrated.
  • Nơi xuất bản: Basel: MDPI AG
  • Ngôn ngữ: English
  • Số nhận dạng: ISSN: 2075-1680
    EISSN: 2075-1680
    DOI: 10.3390/axioms11050241
  • Nguồn: DOAJ Directory of Open Access Journals
    AUTh Library subscriptions: ProQuest Central
    ROAD: Directory of Open Access Scholarly Resources
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