A Multi-Server Heterogeneous Queuing-Inventory System with Class-Dependent Inventory Access

Karumbathil Rasmi, Machuveettil Joseph Jacob, Alexander S. Rumyantsev and Achyutha Krishnamoorthy
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Karumbathil Rasmi: Department of Mathematics, National Institute of Technology Calicut, Kozhikode 673601, Kerala, India
Machuveettil Joseph Jacob: Department of Mathematics, National Institute of Technology Calicut, Kozhikode 673601, Kerala, India
Alexander S. Rumyantsev: Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185910 Petrozavodsk, Russia
Achyutha Krishnamoorthy: Centre for Research in Mathematics, Department of Mathematics, CMS College, Kottayam 686001, Kerala, India

Mathematics, 2021, vol. 9, issue 9, 1-23

Abstract: In this paper, we consider a queuing inventory system with heterogeneous customers of K types arriving according to a marked Markovian arrival process. Each class of customers differs by nature of the service they seek and different priorities are assigned for each class resulting in different levels of inventory admitted to exhaust for customers of each class. A single service node is provided for each class with exponential services having class-dependent service rates. All classes of customers are served from a single source of inventory replenished according to ( s , S ) policy with exponentially distributed lead time. Stability condition and steady state probabilities are obtained by matrix-analytic method. Some important performance measures are also derived. Inventory recycle time was analyzed in detail. Useful cost function and numerical illustrations are also given. The optimization problem is interesting and can be solved in similar real scenario.

Keywords: MMAP[K]; heterogeneous inventory access; multi-server system; queuing-inventory; matrix analytic model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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