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Quasi-birth-and-death processes to determine economic order quantity of a queueing inventory system with impatient customers

Author

Listed:
  • R. Sivasamy
  • Keamogetse Setlhare
  • Olebogeng Mokgware

Abstract

The proposed investigation is an inventory system tied to a single-server M/M/1/N facility that allows impatient customers according to the ordering policy (r, Q). The order is triggered when the stock level drops to a positive integer 'r < Q' for a fixed number 'Q' of units. Here: 1) queueing inventory system (QIS) with lost customers; 2) QIS with back-order are investigated. For each type, we study the long-run moments of the X variable representing the observed queue length, and the Y variable representing observed inventory level. We show that the combined sequence Z = (X, Y) constitutes a level-dependent quasi-birth and death process (LDQBD) in the state space E = {(n, j): n = 0, 1, ..., N, and j = 0, 1, ..., (Q + r)}. We obtain the general probability distribution of the Z process by matrix analysis. Numerical illustrations are provided to find the economic order quantity.

Suggested Citation

  • R. Sivasamy & Keamogetse Setlhare & Olebogeng Mokgware, 2024. "Quasi-birth-and-death processes to determine economic order quantity of a queueing inventory system with impatient customers," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 27(4), pages 531-549.
    • Handle: RePEc:ids:ijmore:v:27:y:2024:i:4:p:531-549
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