Abstract
In this paper we analyze a single server supply chain model in which stocks are kept in both the manufacturer warehouse (production centre) and the retail shop (distribution centre). Arrival of customers to the retail shop form a Poisson process and their service time are exponentially distributed. The maximum stock of the distribution centre is limited to s + Q(=S). When the inventory level depletes to s due to services, it demands Q units at a time from the production centre. The lead time follows an exponential distribution. If the production centre has the required stock on-hand, the items are supplied. Supply of items from the production centre to the distribution centre is done only as a packet of Q units at a time. So if a packet of size Q is not available the distribution centre has to wait till Q units accumulates in the production centre. The production inventory system adopts a (r Q, K Q) policy where the processing of inventory requires a positive random amount of time. Production time for unit item is exponentially distributed. Also we assume that no customer joins the queue when the inventory level in the distribution centre is zero. This assumption leads to an explicit product form solution for the steady state probability vector.
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The authors thank the referees for their critical comments which helped in improving the presentation of the paper.
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Research supported by Kerala State Council for Science, Technology & Environment (No.001/KESS/2013/CSTE)
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Krishnamoorthy, A., Shajin, D. & Lakshmy, B. Product form solution for some queueing-inventory supply chain problem. OPSEARCH 53, 85–102 (2016). https://doi.org/10.1007/s12597-015-0215-8
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DOI: https://doi.org/10.1007/s12597-015-0215-8