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Optimal Control of Service Rates of Discrete-Time (s, Q) Queueing-Inventory Systems with Finite Buffer

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Abstract

This article, we develop an optimal policy to control the service rate of a discrete time queueing-inventory system with finite buffer. The customers arrive according to a Bernoulli process and the service time for the customers are geometric. Whenever the buffer size attains its maximum, any arriving new customers are considered to be lost. The customers are served one by one according to FCFS rule and each customers request random number of items. The inventory is replenished according to a (s, Q) inventory policy with geometric lead time. The main objectives of this article are to determine the service rates to be employed at each slot so that the long run expected cost rate is minimized for fixed inventory level and fixed buffer size and to minimize the expected waiting time for a fixed inventory level and fixed buffer size. The problems are modelled as Markov decision problem. We establish the existence of a stationary policy and employ linear programming method to find the optimal service rates. We provide some numerical examples to illustrate the behaviour of the model.

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Acknowledgments

The research of Ms. L. Iniya is supported by the DST-INSPIRE Fellowship, New Delhi, research award No. DST/INSPIRE Fellowship/[IF190092].

Authors wish to thank the anonymous reviewers for their constructive suggestions which will improve the presentation of the manuscript.

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Authors and Affiliations

  1. School of Mathematics, Madurai Kamaraj University, Madurai, Tamilnadu, India

    L. Iniya & B. Sivakumar

  2. Department of Statistics, Manonmaniam Sundaranar University, Tirunelveli, Tamilnadu, India

    G. Arivarignan

Authors
  1. L. Iniya
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  2. B. Sivakumar
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  3. G. Arivarignan
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Corresponding author

Correspondence to B. Sivakumar.

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The authors declare that there are no commercial or associative interests that constitute a conflict of interest with regard to the work submitted.

Additional information

L. Iniya is pursuing her Ph.D. at the School of Mathematics, Madurai Kamaraj University, Madurai, Tamil Nadu, India, with a DST-INSPIRE Fellowship. She earned her MSc at Madurai Kamaraj University, Madurai. In the master’s degree program, she achieved University First Rank. She is a life member of the ORSI-Kolkata Chapter, India. The areas of her research interest are mathematical modelling of control policies and queueing-inventory systems.

B. Sivakumar received M.Sc. (Mathematics) and Ph.D. from School of Mathematics, Madurai Kamaraj University, India. He has received the Young Scientist Award from DST - SERC Fast Track Scheme in 2008. He has numerous publications in various reputed journals of mathematics and operations research such as European Journal of Operational Research, Computers and Industrial Engineering, Annals of Operations Research, etc. Currently, he is working as an associate professor in the Department of Applied Mathematics, School of Mathematics, Madurai Kamaraj University, Madurai, Tamil Nadu, India. His research interests include stochastic modelling of queueing-inventory systems, control policies in inventory systems, etc.

G. Arivarignan received M.Sc. (Statistics) from Annamalai University, his Ph.D. from Indian Institute of Technology, Madras and D.Sc. from Madurai Kamaraj University. Since 1974, he has worked as assistant professor of statistics in Tamilnadu Collegiate Educational service and joined Madurai Kamaraj University in 1990. His research interests are stochastic modelling and applied statistics. He has numerous publications in various journals of statistics, mathematics and operations research. Currently, he is emeritus professor of statistics in the Department of Statistics, Manonmaniam Sundaranar University, Tirunelveli, Tamil Nadu, India.

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Iniya, L., Sivakumar, B. & Arivarignan, G. Optimal Control of Service Rates of Discrete-Time (s, Q) Queueing-Inventory Systems with Finite Buffer. J. Syst. Sci. Syst. Eng. 33, 261–280 (2024). https://doi.org/10.1007/s11518-024-5599-7

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  • DOI: https://doi.org/10.1007/s11518-024-5599-7

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