Abstract
A queueing-inventory system, with the item given with probability γ to a customer at his service completion epoch, is considered in this paper. Two control policies, (s,Q) and (s,S) are discussed. In both cases we obtain the joint distribution of the number of customers and the number of items in the inventory as the product of their marginals under the assumption that customers do not join when inventory level is zero. Optimization problems associated with both models are investigated and the optimal pairs (s,S) and (s,Q) and the corresponding expected minimum costs are obtained. Further we investigate numerically an expression for per unit time cost as a function of γ. This function exhibit convexity property. A comparison with Schwarz et al. (Queueing Syst. 54:55–78, 2006) is provided. The case of arbitrarily distributed service time is briefly indicated.
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Acknowledgements
Manikandan’s research is supported by the University Grants Commission, Govt. of India, under RGNF Scheme (No. F.16-1041 (SC)/2008(SA-III)). The authors thank the reviewers and editors for helpful comments on the earlier version of this paper that improved its presentation.
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Krishnamoorthy, A., Manikandan, R. & Lakshmy, B. A revisit to queueing-inventory system with positive service time. Ann Oper Res 233, 221–236 (2015). https://doi.org/10.1007/s10479-013-1437-x
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DOI: https://doi.org/10.1007/s10479-013-1437-x