International Journal of Mathematics Trends and Technology
Volume 56 | Number 6 | Year 2018 | Article Id. IJMTT-V56P556 | DOI : https://doi.org/10.14445/22315373/IJMTT-V56P556
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.
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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
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