Queueing-Inventory with One Essential and m Optional Items with Environment Change Process Forming Correlated Renewal Process (MEP)

Jaison Jacob, Dhanya Shajin, Achyutha Krishnamoorthy, Vladimir Vishnevsky and Dmitry Kozyrev
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Jaison Jacob: Department of Mathematics, St. Aloysius College, Elthuruth, Thrissur 680611, India
Dhanya Shajin: Department of Mathematics, Sree Narayana College, Chempazhanthy, Thiruvanathapuram 695587, India
Achyutha Krishnamoorthy: Centre for Research in Mathematics, CMS College, Kottayam 686001, India
Vladimir Vishnevsky: V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 65 Profsoyuznaya Street, 117997 Moscow, Russia
Dmitry Kozyrev: V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, 65 Profsoyuznaya Street, 117997 Moscow, Russia

Mathematics, 2021, vol. 10, issue 1, 1-26

Abstract: We consider a queueing inventory with one essential and m optional items for sale. The system evolves in environments that change randomly. There are n environments that appear in a random fashion governed by a Marked Markovian Environment change process. Customers demand the main item plus none, one, or more of the optional items, but were restricted to at most one unit of each optional item. Service time of the main item is phase type distributed and that of optional items have exponential distributions with parameters that depend on the type of the item, as well as the environment under consideration. If the essential item is not available, service will not be provided. The lead times of optional and main items have exponential distributions having parameters that depend on the type of the item. The condition for stability of the system is analyzed by considering a multi-dimensional continuous time Markov chain that represent the evolution of the system. Under this condition, various performance characteristics of the system are derived. In terms of these, a cost function is constructed and optimal control policies of the different types of commodities are investigated. Numerical results are provided to give a glimpse of the system performance.

Keywords: essential item; optional item(s); random environment; Markovian arrival process; phase-type distribution; marked Markovian environment change process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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