Finite source inventory system with negative customers

M. Bhuvaneshwari

doi:https://doi.org/10.14445/22315373/IJMTT-V56P556

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 56 | Number 6 | Year 2018 | Article Id. IJMTT-V56P556 | DOI : https://doi.org/10.14445/22315373/IJMTT-V56P556

Finite source inventory system with negative customers

M. Bhuvaneshwari

Citation :

M. Bhuvaneshwari, "Finite source inventory system with negative customers," International Journal of Mathematics Trends and Technology (IJMTT), vol. 56, no. 6, pp. 419-429, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V56P556

Abstract

We consider a finite source queueing-inventory system with a service facility, wherein the demand of a customer is satisfied only after performing some service on the item which is assumed to be of random duration. An arriving customer turns out to be an ordinary customer with probability r and a negative customer with probability (1 − r), (0 ≤ r ≤ 1). An ordinary customer, on arrival, joins the queue and the negative customer does not join the queue and takes away one waiting customer if any. The inventory is replenished according to an (s, S) policy and the replenishing times are assumed to be exponentially distributed. The server provides two types of services - one with essential service and the other with a second optional service. The service times of the 1st (essential) and 2nd (optional) services are independent and exponentially distributed. The service process is subject to interruptions, which occurs according to a Poisson process. The interrupted server is repaired at an exponential rate. The joint probability distribution of the number of customers in the system and the inventory level is obtained in the steady state case. Various system performance measures are derived and the total expected cost rate is computed under a suitable cost structure.

Keywords

(s, S) policy, Inventory with service time, Markov process, Negative Customers

References

[1] Berman, O. and Kim, E. (1999). Stochastic models for inventory management at service facility, Stochastic Models, Vol.15, No.4, 695-718.
[2] Berman, O. and Kim, E. (2004). Dynamic inventory strategies for profit maximization in a service facility with stochastic service, Mathematical Methods of Operations Research, Vol.60, No.3, 497-521.
[3] Berman, O. and Kim, E. (2001). Dynamic order replenishment policy in internet-based supply chains, Mathematical Methods of Operations Research, Vol.53, No.3, 371-390.
[4] Berman, O. and Sapna, K.P. (2000). Inventory management at service facility for systems with arbitrarily distributed service times, Communications in Statistics. Stochastic Models, Vol.16, No.3, 343-360.
[5] Berman, O. and Sapna, K.P. (2001). Optimal control of service for facilities holding inventory, Computers and Operations Research, Vol.28, No.5, 429-441.
[6] Jeganathan K. and Periyasamy, C (2014), A perishable inventory system with repeated customers and server interruptions, Applied Mathematics and Information Sciences Letters, Vol. 2(2), 1-11. 10
[7] Krishnamoorthy, A., & Anbazhagan, N (2008), Perishable inventory system at service facility with N policy, Stochastic Analysis and Applications, 26(1), 1-17.
[8] Krishnamoorthy, A., Nair, S.S., & Narayanan, V.C., (2010), An inventory model with server interruptions, Opsearch, 25(1) 1-17.
[9] Krishnamoorthy, A., Nair, S.S., & Narayanan, V.C., (2012), An inventory model with server interruptions and retrials, Operations Research International Journal, 12(2) 151 - 171.
[10] Schwarz, M., Sauer, C., Daduna, H., Kulik, R. and Szekli, R. (2006). M/M/1 queueing systems with inventory, Queueing Systems Theory and Applications, Vol.54, No.1, 55-78.
[11] Ross, S. M. Introduction to Probability Models, Harcourt Asia PTE Ltd, Singapore, 2000.