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A PH Distributed Production Inventory Model with Different Modes of Service and MAP Arrivals

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Applied Probability and Stochastic Processes

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Abstract

This paper studies a production inventory model with retrial of customers under (s, S) policy. The arrival of customers is according to a Markovian Arrival Process with representation (D 0, D 1) and service times follow an exponential distribution. The production process follows a phase-type distribution. When the inventory level reduces to a pre-assigned level s due to demands, production starts and service is given at a reduced rate. This reduced rate continuous up to the zero level of inventory. The arriving customers are directed to a buffer of finite capacity equal to the current inventory level. An arriving customer, who notices the buffer full, proceeds to an orbit of infinite capacity with some probability and decides to leave the system with the complementary probability. An orbiting customer may retry from the orbit and inter-retrial times are exponentially distributed with linear rate. Various system performance measures of the model are defined. A suitable cost function is constructed and analyzed algorithmically. The optimum (s, S) pair is obtained. The effect of correlation between two successive inter-arrival times is also analyzed.

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Acknowledgements

Salini S. Nair acknowledges the financial support of University Grants Commission of India under Faculty Development Programme F.No. FIP/12th Plan/KLMG045 TF07/2015.

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Authors and Affiliations

  1. PG and Research Department of Mathematics, St. Peter’s College, Kolenchery, Kerala, India

    Salini S. Nair & K. P. Jose

Authors
  1. Salini S. Nair
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  2. K. P. Jose
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Editor information

Editors and Affiliations

  1. Department of Mathematics, CMS College, Kottayam, India

    V. C. Joshua

  2. Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

    S. R. S. Varadhan

  3. Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevsky

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Nair, S.S., Jose, K.P. (2020). A PH Distributed Production Inventory Model with Different Modes of Service and MAP Arrivals. In: Joshua, V., Varadhan, S., Vishnevsky, V. (eds) Applied Probability and Stochastic Processes. Infosys Science Foundation Series(). Springer, Singapore. https://doi.org/10.1007/978-981-15-5951-8_16

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