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

R. Sivasamy, Keamogetse Setlhare and Olebogeng Mokgware

International Journal of Mathematics in Operational Research, 2024, vol. 27, issue 4, 531-549

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.

Keywords: queueing inventory; queue length; inventory level; customer impatience; stationary distribution; expected cost; economic order. (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.inderscience.com/link.php?id=138466 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ids:ijmore:v:27:y:2024:i:4:p:531-549

Access Statistics for this article

More articles in International Journal of Mathematics in Operational Research from Inderscience Enterprises Ltd
Bibliographic data for series maintained by Sarah Parker ().