Control Systems and Computers, N3, 2018, Article 6
DOI: https://doi.org/10.15407/usim.2018.03.060
Upr. sist. maš., 2018, Issue 3 (275), pp. 60-68.
UDK 004.94
Mammad SHAHMALIYEV, PhD student, National Aviation Academy of Azerbaijan, Xudu Mammadov str. 38, 122, Baku, AZ1129, Azerbaaijan, mamed.shahmaliyev@gmail.com
SIMULATION MODEL OF INFINITE PERISHABLE QUEUEING INVENTORY SYSTEM WITH FEEDBACK
Perishable Queuing Inventory system with positive service time and customer feedback is considered. The system applies Variable Size Order policy for the inventory replenishment. Stochastic simulation method is used to calculate the system performance measures and find its stationary distribution. The dependence of performance measures on the reorder level is illustrated and analyzed using the numerical experiments.
Download full text! (In English).
Keywords: perishable queuing-inventory system, infinite three-dimensional Markov Chain, simulation algorithm, VSO-policy, numerical experiments.
REFERENCES
- Artalejo, J.R., Krishnamoorthy, A., Lopez-Herrero, M.J. 2006. “Numerical analysis of (s, S) inventory system with repeated attempts”. Annals of Operations Research, 141, pp. 67–83.
https://doi.org/10.1007/s10479-006-5294-8 - USHAKUMARI, P.V., 2006. “On (s, S) inventory system with random lead time and repeated demands”. Journal of Applied Mathematics and Stochastic Analysis, ID: 81508, pp. 22.
https://doi.org/10.1155/JAMSA/2006/81508 - Lopez-Herrero, M.J., 2010. “Waiting time and other first-pasage time measures in an (s, S) inventory system with repeated attempts and finite retrial group”. Computers and Operations Research, 37, pp. 1256–1261
https://doi.org/10.1016/j.cor.2009.02.011 - ANBAZHAGAN. N., WANG, J., GOMATHI, D., 2013. “Base stock policy with retrial demands. Applied Mathematical Modelling”, 37, pp. 4464–4473.
https://doi.org/10.1016/j.apm.2012.09.005 - Krishnamoorthy, A., Jose, K.P., 2007. “Comparision of inventory systems with service, positive lead-time, loss, and retrial of customers”. Journal of Applied Mathematics and Stochastic Analysis. Hindawi Publishing Corparation, ID: 37848, pp. 23.
- Nair, A.N., Jacob, M.J., 2014. (s, S) inventory system with positive service time and retrial of demands: an approach through multi-server queues. ISRN Operations Research. Hindawi Publishing Corparation. ID: 596031, pp. 6.
- YADAVALLI, .S.S., ANBAZHAGAN, N., JEGANATHAN, K., 2015. “A retrial inventory system with impatient customers”. Applied Mathematics and Information Science, 9, pp. 637–650.
- Amirthakodi, M., Sivakumar, B., 2015. “An inventory system with service facility and finite orbit for feedback customers”. OPSEARCH, 52(2), pp. 225–255.
https://doi.org/10.1007/s12597-014-0182-5 - Manikandan, R., Nair, S.S., 2017. M/M/1/1 queuing-inventory system with retrial of unsatisfied customers. Communications in Applied Analysis, 21(2), pp. 217–236.
- Neuts, M.F., 1981. “Matrix-geometric solutions in stochastic models: An algorithmic approach”. Baltimore: John Hopkins University Press, pp. 332.
- Manuel, P., Sivakumar, B., Arivarignan, G., 2008. “A perishable inventory system with service facilities and retrial customers”. Computers and Industrial Engineering, 54, pp. 484–501.
https://doi.org/10.1016/j.cie.2007.08.010 - Sivakumar, B., 2011. “An inventory system with retrial demands and multiple server vacation”. Quality Technology and Quantitative Management, 8 (2), pp. 125–146.
https://doi.org/10.1080/16843703.2011.11673252 - Manuel, P., Sivakumar, B., Arivarignan, G., 2008. “A perishable inventory system with service facilities and retrial customers”. Computers and Industrial Engineering, 54, pp. 484–501.
https://doi.org/10.1016/j.cie.2007.08.010 - Krishnamoorthy, A., Manikandan, R., Lakshmy, B., 2015. “Revisit to queuing-inventory system with positive service time”, Annals of Operations Research, 233, pp. 221–236.
https://doi.org/10.1007/s10479-013-1437-x - Melikov, A.Z., Ponomarenko, L.A., Shahmaliyev, M.O., 2017. “Analysis of perishable queuing-inventory systems with different types of requests”. Journal of Automation and Information Sciences, 49 (9), pp. 42–60.
https://doi.org/10.1615/JAutomatInfScien.v49.i9.40 - Melikov, A.Z., Ponomarenko, L.A., Rustamov, A.M., 2017. “Approximate analysis of queuing-inventory system with earlier and delayed vacations”. Automation and Remote Control, 78 (11), pp. 1991–2003.
https://doi.org/10.1134/S0005117917110054 - Mitrani, I., Chakka, R., 1995. “Spectral expansion solution for a class of Markov models: application and comparison with the matrix-geometric method”. Performance Evaluation, 23, pp. 241–260.
https://doi.org/10.1016/0166-5316(94)00025-F - Melikov, A.Z., Ponomarenko, L.A., Shahmaliyev, M.O., 2016. “Models of perishable queuing-inventory systems with repeated customers”. Journal of Automation and Information, 48 (6), pp. 22–38.
https://doi.org/10.1615/JAutomatInfScien.v48.i6.30 - Gillespie, D.T., 1976. “A General method for numerically simulating the stochastic time evolution”. Journal of Computational Physics, 22, pp. 403–434.
https://doi.org/10.1016/0021-9991(76)90041-3 - Banks, H.T., Broido, A., Canter, B., Gayvert, K., Hu, SH., Joyner, M.L., Link, K., 2011. “Simulation algorithms for continuous time Markov chain models”. North Carolina State University. Center for Research in Scientific Computation, CRSC-TR, pp. 11–17.
Received 27.09.2018
