Geodesic
A Markovian two commodity queueing-inventory system with compliment item and classical retrial facility
Ural mathematical journal, Tome 8 (2022) no. 1, pp. 90-116 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper explores the two-commodity (TC) inventory system in which commodities are classified as major and complementary items. The system allows a customer who has purchased a free product to conduct Bernoulli trials at will. Under the Bernoulli schedule, any entering customer will quickly enter an orbit of infinite capability during the stock-out time of the major item. The arrival of a retrial customer in the system follows a classical retrial policy. These two products' re-ordering process occurs under the $(s, Q)$ and instantaneous ordering policies for the major and complimentary items, respectively. A comprehensive analysis of the retrial queue, including the system's stability and the steady-state distribution of the retrial queue with the stock levels of two commodities, is carried out. The various system operations are measured under the stability condition. Finally, numerical evidence has shown the benefits of the proposed model under different random situations.
Keywords: Markov process, infinite orbit, waiting time.
Mots-clés : compliment item 
@article{UMJ_2022_8_1_a8,
     author = {M. Nithya and C. Sugapriya and S. Selvakumar and K. Jeganathan and T. Harikrishnan},
     title = {A {Markovian} two commodity queueing-inventory system with compliment item and classical retrial facility},
     journal = {Ural mathematical journal},
     pages = {90--116},
     year = {2022},
     volume = {8},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2022_8_1_a8/}
}
TY  - JOUR
AU  - M. Nithya
AU  - C. Sugapriya
AU  - S. Selvakumar
AU  - K. Jeganathan
AU  - T. Harikrishnan
TI  - A Markovian two commodity queueing-inventory system with compliment item and classical retrial facility
JO  - Ural mathematical journal
PY  - 2022
SP  - 90
EP  - 116
VL  - 8
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UMJ_2022_8_1_a8/
LA  - en
ID  - UMJ_2022_8_1_a8
ER  - 
%0 Journal Article
%A M. Nithya
%A C. Sugapriya
%A S. Selvakumar
%A K. Jeganathan
%A T. Harikrishnan
%T A Markovian two commodity queueing-inventory system with compliment item and classical retrial facility
%J Ural mathematical journal
%D 2022
%P 90-116
%V 8
%N 1
%U http://geodesic.mathdoc.fr/item/UMJ_2022_8_1_a8/
%G en
%F UMJ_2022_8_1_a8
M. Nithya; C. Sugapriya; S. Selvakumar; K. Jeganathan; T. Harikrishnan. A Markovian two commodity queueing-inventory system with compliment item and classical retrial facility. Ural mathematical journal, Tome 8 (2022) no. 1, pp. 90-116. http://geodesic.mathdoc.fr/item/UMJ_2022_8_1_a8/

[1] Abate J., Whitt W., “Numerical inversion of Laplace transforms of probability distributions”, ORSA J. Comput., 7:1 (1995), 36–43 | DOI | Zbl

[2] Anbazhagan N., Arivarignan G., “Two commodity continuous review inventory system with coordinated reorder policy”, Int. J. Inf. Manag. Sci., 11:3 (2000), 19–30 | MR | Zbl

[3] Anbazhagan N., Arivarignan G., “Two commodity inventory system with individual and joint ordering policies”, Int. J. Manag. Syst., 19:2 (2003), 129–144

[4] Anbazhagan N., Arivarignan G., “Analysis of two commodity Markovian inventory system with lead time”, Korean J. Comput. Appl. Math., 8:2 (2001), 427, 427–438 | DOI | MR | Zbl

[5] Anbazhagan N., Jeganathan K., “Two-commodity Markovian inventory system with compliment and retrial demand”, J. Adv. Math. Comput. Sci., 3:2 (2013), 115–134 | DOI | MR

[6] Arivarignan G., Keerthana M., Sivakumar B., “A production inventory system with renewal and retrial demands”, Applied Probability and Stochastic Processes, Infosys Sci. Found. Ser., eds. Joshua V., Varadhan S., Vishnevsky V., Springer, Singapor, 2020, 129–142 | DOI | MR | Zbl

[7] Artalejo J. R., Krishnamoorthy A., Lopez-Herrero M. J., “Numerical analysis of $(s,S)$ inventory systems with repeated attempts”, Ann. Oper. Res., 141 (2006), 67–83 | DOI | MR | Zbl

[8] Benny B., Chakravarthy S. R., Krishnamoorthy A., “Queueing-inventory system with two commodities”, J. Indian Soc. Probab. Stat., 19:1 (2018), 437–454 | DOI

[9] Chakravarthy S. R., Krishnamoorthy A., Joshua V. C., “Analysis of a multi-server retrial queue with search of customers from the orbit.”, Perform. Eval., 63:8 (2006), 776–798 | DOI

[10] Goyal S. K., Satir A. T., “Joint replenishment inventory control: deterministic and stochastic models”, European J. Oper. Res., 38:1 (1989), 2–13 | DOI | MR | Zbl

[11] Jeganathan K., Reiyas M. A., Padmasekaran S., Lakshmanan K., “An $M/E_K/1/N$ queueing-inventory system with two service rates based on queue lengths”, Int. J. Appl. Comput. Math., 3:1 (2017), 357–386 | DOI | MR

[12] Jeganathan K., Melikov A. Z., Padmasekaran S. et al., “A stochastic inventory model with two queues and a flexible server”, Int. J. Appl. Comput. Math., 5:1 (2019), 21, 1–27 | DOI | MR | Zbl

[13] Jeganathan K., Reiyas M. A., “Two parallel heterogeneous servers Markovian inventory system with modified and delayed working vacations.”, Math. Comput. Simulation, 172 (2020), 273–304 | DOI | MR | Zbl

[14] Jeganathan K., Harikrishnan T., Selvakumar S. et al., “Analysis of interconnected arrivals on queueing-inventory system with two multi-server service channels and one retrial facility”, Electronics, 10:5 (2021), 1—35 | DOI

[15] Jose K. P., Reshmi, “A production inventory model with deteriorating items and retrial demands”, OPSEARCH, 58 (2021), 71–82, S. pp. | DOI | MR | Zbl

[16] Kalpakam S., Arivarignan G., “A coordinated multicommodity $(s, S)$ inventory system”, Math. Comput. Model., 18:11 (1993), 69–73 | DOI | Zbl

[17] Keerthana M., Saranya N., Sivakumar B., “A stochastic queueing-inventory system with renewal demands and positive lead time.”, Eur. J. Ind. Eng., 14:4 (2020), 443–484 | DOI

[18] Krishnamoorthy A., Iqbal Basha R., Lakshmy B., “Analysis of two commodity inventory problem”, Int. J. Inf. Manag. Sci., 5:1 (1994), 127–136 | MR | Zbl

[19] Krishnamoorthy A., Merlymol J., Ravindranathan., “Analysis of a bulk demand two commodity inventory problem”, Calcutta Stat. Assoc. Bull., 49:1–2 (1999), 193–194. | DOI | MR | Zbl

[20] Krishnamoorthy A., Manikandan R., Lakshmy B., “A revisit to queueing-inventory system with positive service time.”, Ann. Oper. Res., 233 (2015), 221–236 | DOI | MR | Zbl

[21] Krishnamoorthy A., Shajin D., Lakshmy B., “$GI/M/1$ type queueing-inventory systems with postponed work, reservation, cancellation and common life time”, Indian J. Pure Appl. Math., 47:2 (2016), 357–388 | DOI | MR | Zbl

[22] Krishnamoorthy A., Shajin D., “$MAP/PH/1$ retrial queueing-inventory system with orbital search and reneging of customers”, Analytical and Computational Methods in Probability Theory (ACMPT 2017), v. 10684, Lecture Notes in Comput. Sci., eds. Rykov V., Singpurwalla N., Zubkov A., Springer, Cham, 2017, 158–171 | DOI | Zbl

[23] Lakshmanan K., Padmasekaran S., Jeganathan K., “Mathematical analysis of queueing-inventory model with compliment and multiple working vacations.”, Int. J. Eng. Adv. Technol., 8:6 (2019), 4239–4240 | DOI

[24] Neuts M. F., Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, Dover Publication Inc., New York, 1994, 332 pp. | MR

[25] Senthil Kumar P., “A discrete time two commodity inventory system”, Int. J. Engrg. Res. Technol., 5:1 (2016), 708–719 | DOI

[26] Shajin D., Krishnamoorthy A., Dudin A. N. et al., “On a queueing-inventory system with advanced reservation and cancellation for the next $K$ time frames ahead: the case of overbooking”, Queueing Syst., 94 (2020), 3–37 | DOI | MR | Zbl

[27] Sivazlian B. D., “Stationary analysis of a multicommodity inventory system with interacting set-up costs”, SIAM J. App. Math., 20 (1971), 264–278 https://www.jstor.org/stable/2099925?seq=1 | DOI | MR | Zbl

[28] Sivakumar B., Anbazhagan N., Arivarignan G., “A two-commodity perishable inventory system”, ORiON, 21:2 (2005), 157–172 | DOI

[29] Sivakumar B., Anbazhagan N., Arivarignan G., “Two commodity continuous review perishable inventory system”, Int. J. Inf. Manag. Sci., 17:3 (2006), 47–64 | MR | Zbl

[30] Sivakumar B., Anbazhagan N., Arivarignan G., “Two-commodity inventory system with individual and joint ordering policies and renewal demands”, Stoch. Anal. Appl., 25:6 (2007), 1217–1241 | DOI | MR | Zbl

[31] Sivakumar B., “Two-commodity inventory system with retrial demand”, Eur. J. Oper. Res., 187:1 (2008), 70–83 | DOI | MR | Zbl

[32] {Ushakumari, “On $(s , S)$ inventory system with random lead time and repeated demands”, J. Appl. Math. Stochastic Anal., 2006 (2006), 81508, 1–22, V.} pp. | DOI | MR

[33] Yadavalli V. S. S., Anbazhagan N., Arivarignan G., “A two-commodity stochastic inventory system with lost sales”, Stoch. Anal. Appl., 22:2 (2004), 479–497 | DOI | MR | Zbl

[34] Yadavalli V. S. S., Arivarignan G., Anbazhagan N., “Two commodity coordinated inventory system with Markovian demand”, Asia-Pac. J. Oper. Res., 23:4 (2006), 497–508 | DOI | MR | Zbl

[35] Yadavalli V. S. S., Sivakumar B., Arivarignan G., Olufemi Adetunji., “A finite source multi-server inventory system with service facility”, Comput. Ind. Eng., 63 (2012), 739–753 | DOI

[36] Yadavalli V. S. S., Adetunji O., Sivakumar B., Arivarignan G., “Two-commodity perishable inventory system with bulk demand for one commodity”, S. Afr. J. Ind. Eng., 21:1 (2010), 137–155 | DOI | MR