Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

Serife Ozkar, Agassi Melikov and Janos Sztrik ()
Additional contact information
Serife Ozkar: Department of International Trade and Logistics, Balikesir University, Balikesir 10145, Turkey
Agassi Melikov: Department of Mathematics, Baku Engineering University, Baku 0101, Azerbaijan
Janos Sztrik: Faculty of Informatics, University of Debrecen, 4032 Debrecen, Hungary

Mathematics, 2023, vol. 11, issue 23, 1-24

Abstract: We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to the Poisson process and instantly destroy all items in the inventory. The arrivals of the consumer customers follow a Markovian arrival process and they can be queued in an infinite buffer. The service time of a consumer customer follows a phase-type distribution. The system receives negative customers which have Poisson flows and as soon as a negative customer comes into the system, he causes a consumer customer to leave the system, if any. One of two inventory policies is used in the systems: either ( s , S ) or ( s , Q ) . If the inventory level is zero when a consumer customer arrives, then this customer is either lost (lost sale) or joins the queue (backorder sale). The system is formulated by a four-dimensional continuous-time Markov chain. Ergodicity condition for both systems is established and steady-state distribution is obtained using the matrix-geometric method. By numerical studies, the influence of the distributions of the arrival process and the service time and the system parameters on performance measures are deeply analyzed. Finally, an optimization study is presented in which the criterion is the minimization of expected total costs and the controlled parameter is warehouse capacity.

Keywords: queueing-inventory system; catastrophe; negative customer; ( s , S )-type policy; ( s , Q )-type policy; matrix geometric method; MAP arrival; phase-type distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/23/4854/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/23/4854/ (text/html)

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:gam:jmathe:v:11:y:2023:i:23:p:4854-:d:1292903

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().