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A perishable inventory system with service facility and finite source. (English) Zbl 1426.90026
Summary: In this article, we consider a continuous review ($$s, S$$) perishable 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. We also assume that the demands are generated by a finite homogeneous population. The service time, the lead time are assumed to have Phase type distribution. The life time of the item is assumed to have exponential distributions. The joint distribution of the number of customers in the system and the inventory level is obtained in the steady state case. The Laplace-Stieltjes transform of the waiting time of the tagged customer is derived. Various system performance measures are derived and the total expected cost rate is computed under a suitable cost structure. The results are illustrated numerically.

##### MSC:
 90B05 Inventory, storage, reservoirs 90B22 Queues and service in operations research 60K25 Queueing theory (aspects of probability theory)
##### Keywords:
$$(s; S)$$ policy; positive lead time; finite source
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##### References:
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