A MAP/PH/1 Perishable Inventory System with Dependent Retrial Loss
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A MAP/PH/1 Perishable Inventory System with Dependent Retrial Loss P. S. Reshmi1 · K. P. Jose1 Accepted: 7 October 2020 © Springer Nature India Private Limited 2020
Abstract This paper considers a continuous review perishable inventory system with an infinite orbit. The replenishment of items in the inventory is governed by (s, Q) policy. The Markovian Arrival Process characterizes the arrival pattern of primary customers and the service time follows phase-type distribution. Inventoried items are subject to decay with some preassigned linear rate. The items are purchased from an outside source and lead time is exponentially distributed. An unsatisfied primary customer may enter an orbit or exit the system with a predetermined probability. The retrial customers, those who entered into the orbit, try to access the idle server with a linear rate. An unsatisfied retrial customer may enter or exit the orbit with prefixed probability based on the inventory level. Stationary probability vectors are obtained using the Matrix Analytic method. Numerical optimization of the profit function is carried out for different parameter values. Keywords Perishable inventory · Markovian arrival process · Phase type distribution · Matrix analytic method · Inventory dependent retrial Mathematics Subject Classification 60K25 · 90B05 · 91B70
Introduction In the early period of modelling, it was assumed that all the stored items have an infinite lifetime, but the real situation is different. Most of the inventoried items have a shelf life like food stuff, medicinal drugs and implants, chemical substances, and so on. Therefore, the deterioration of items cannot be exempted from inventory models. In view of this, we attach a retrial inventory system with perishable items where the retrial loss is dependent on inventory. The study of perishable inventory systems with retrial facility has been getting significant attention from many researchers, and the following literature provides a brief outlook of
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K. P. Jose [email protected] P. S. Reshmi [email protected]
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P. G. & Research Dept. of Mathematics, St.Peter’s College, Kolenchery, Kerala 682 311, India 0123456789().: V,-vol
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Int. J. Appl. Comput. Math
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such systems. Laxmi and Soujanya [7] observed a perishable inventory system with two types of arriving customers and the arrival pattern follows the Markovian arrival process. The customers are offered to join a finite orbit when the server is on vacation. Items stored are decaying and the decay time is exponentially distributed. Periyasamy [13] deals with a continuous review perishable inventory system governed by (s, S) policy. The demands occur from a finite source to a single server. The server goes for vacation when the inventory level is zero in an exponentially distributed manner. The arriving customer in server vacation period occupy in the orbit and compete for their demand in exponentially distributed time. Manual et al.[8] considered a single server queueing-inventory system wit
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