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Multi-Server Queuing Production Inventory System with Emergency Replenishment

Author

Listed:
  • Dhanya Shajin

    (Department of Mathematics, S. N. College, Chempazhanthy 695587, Kerala, India)

  • Achyutha Krishnamoorthy

    (Centre for Research in Mathematics, CMS College, Kottayam 686001, Kerala, India)

  • Agassi Z. Melikov

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

  • Janos Sztrik

    (Department of Informatics and Networks, Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary)

Abstract

We consider a multi-server production inventory system with an unlimited waiting line. Arrivals occur according to a non-homogeneous Poisson process and exponentially distributed service time. At the service completion epoch, one unit of an item in the on-hand inventory decreases with probability δ , and the customer leaves the system without taking the item with probability ( 1 − δ ) . The production inventory system adopts an ( s , S ) policy where the processing of inventory requires a positive random amount of time. The production time for a unit item is phase-type distributed. Furthermore, assume that an emergency replenishment of one item with zero lead time takes place when the on-hand inventory level decreases to zero. The emergency replenishment is incorporated in the system to ensure customer satisfaction. We derive the stationary distribution of the system and some main performance measures, such as the distribution of the production on/off time in a cycle and the mean emergency replenishment cycle time. Numerical experiments are conducted to illustrate the system performance. A cost function is constructed, and we examine the optimal number of servers to be employed. Furthermore, we numerically calculate the optimal values of the production starting level and maximum inventory level.

Suggested Citation

  • Dhanya Shajin & Achyutha Krishnamoorthy & Agassi Z. Melikov & Janos Sztrik, 2022. "Multi-Server Queuing Production Inventory System with Emergency Replenishment," Mathematics, MDPI, vol. 10(20), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3839-:d:944840
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    References listed on IDEAS

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    1. O. Berman & K.P. Sapna, 2002. "Optimal service rates of a service facility with perishable inventory items," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(5), pages 464-482, August.
    2. Alfares, Hesham K., 2007. "Inventory model with stock-level dependent demand rate and variable holding cost," International Journal of Production Economics, Elsevier, vol. 108(1-2), pages 259-265, July.
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    Cited by:

    1. Jai Deep Pandey & Geetanjali Sharma, 2024. "A production supply chain inventory model with queuing application and carbon emissions under learning effect," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 548-569, June.
    2. Kathirvel Jeganathan & Thanushkodi Harikrishnan & Kumarasankaralingam Lakshmanan & Agassi Melikov & Janos Sztrik, 2023. "Modeling of Junior Servers Approaching a Senior Server in the Retrial Queuing-Inventory System," Mathematics, MDPI, vol. 11(22), pages 1-31, November.

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