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Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse

Author

Listed:
  • Agassi Melikov

    (Institute of Control Systems, National Academy of Science, Baku AZ 1141, Azerbaijan)

  • Laman Poladova

    (Institute of Control Systems, National Academy of Science, Baku AZ 1141, Azerbaijan)

  • Sandhya Edayapurath

    (Jyothi Engineering College, APJ Abdul Kalam Technological University, Thrissur 680009, Kerala, India)

  • Janos Sztrik

    (Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary)

Abstract

In this paper, we studied single-server models of queuing-inventory systems (QIS) with catastrophes in the warehouse part and negative customers ( n -customers) in service facility. Consumer customers ( c -customers) that arrived to buy inventory can be queued in an infinite buffer. Under catastrophes, all inventory of the system is destroyed but customers in the system (on server or in buffer) are still waiting for replenishment of stocks. Upon arrival of n -customer one c-customer is pushed out, if any. One of two replenishment policies (RP) can be used in the system: either ( s , S ) or randomized. In the investigated QISs, a hybrid service scheme was used: if upon arrival of the c-customer, the inventory level is zero, then according to the Bernoulli scheme, this customer is either lost (lost sale scheme) or joining the queue (backorder scheme). Mathematical models of the investigated QISs were constructed as two-dimensional Markov chains (2D MC). Ergodicity conditions of the investigated QISs were obtained, and the matrix-analytic method (MAM) was used to calculate the steady-state probabilities of the constructed 2D MCs. Formulas for performance measures were found and the results of numerical experiments are presented.

Suggested Citation

  • Agassi Melikov & Laman Poladova & Sandhya Edayapurath & Janos Sztrik, 2023. "Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2380-:d:1151472
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    References listed on IDEAS

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    1. Agassi Melikov & Ramil Mirzayev & Sajeev S. Nair, 2022. "Double Sources Queuing-Inventory System with Hybrid Replenishment Policy," Mathematics, MDPI, vol. 10(14), pages 1-16, July.
    2. G. Arul Freeda Vinodhini & V. Vidhya, 2016. "Computational Analysis of Queues with Catastrophes in a Multiphase Random Environment," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-7, August.
    3. Yuying Zhang & Dequan Yue & Wuyi Yue, 2022. "A queueing-inventory system with random order size policy and server vacations," Annals of Operations Research, Springer, vol. 310(2), pages 595-620, March.
    4. A. Krishnamoorthy & R. Manikandan & B. Lakshmy, 2015. "A revisit to queueing-inventory system with positive service time," Annals of Operations Research, Springer, vol. 233(1), pages 221-236, October.
    5. Mustafa Demircioglu & Herwig Bruneel & Sabine Wittevrongel, 2021. "Analysis of a Discrete-Time Queueing Model with Disasters," Mathematics, MDPI, vol. 9(24), pages 1-22, December.
    6. Zhaotong Lian & Liming Liu & Marcel F. Neuts, 2005. "A Discrete-Time Model for Common Lifetime Inventory Systems," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 718-732, August.
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    Cited by:

    1. Farida F. Galimulina & Naira V. Barsegyan, 2024. "Application of Mass Service Theory to Economic Systems Optimization Problems—A Review," Mathematics, MDPI, vol. 12(3), pages 1-18, January.
    2. Serife Ozkar & Agassi Melikov & Janos Sztrik, 2023. "Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies," Mathematics, MDPI, vol. 11(23), pages 1-24, December.
    3. Agassi Melikov & Laman Poladova & Janos Sztrik, 2024. "Queuing-Inventory System with Catastrophes in the Warehouse: Case of Rare Catastrophes," Mathematics, MDPI, vol. 12(6), pages 1-19, March.
    4. Jung Woo Baek, 2024. "On the Control Policy of a Queuing–Inventory System with Variable Inventory Replenishment Speed," Mathematics, MDPI, vol. 12(2), pages 1-19, January.

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