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Replacement of failed items in a two commodity retrial queueing-inventory system with multi-component demand and

K Jeganathan1, V Anzen Koffer1, K Lakshmanan2

  • 1Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, 600005, India.

Heliyon
|January 31, 2024
PubMed
Summary

This study shows that replacing failed items in a two-commodity queueing-inventory system significantly improves operational efficiency and reduces costs. Strategic replacement policies enhance profitability in dynamic commercial settings.

Keywords:
Classical retrial policyMatrix-geometric solutionStability conditionSteady state probability vector

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Area of Science:

  • Operations Research
  • Queueing Theory
  • Inventory Management

Background:

  • Dynamic commercial environments necessitate efficient inventory management, particularly for replacing failed items.
  • Two-commodity systems with complimentary items and pooled storage present unique inventory challenges.
  • Server vacations and multi-component demand add complexity to queueing-inventory models.

Purpose of the Study:

  • To analyze a two-commodity retrial queueing-inventory system with vacation interruption and a replacement policy.
  • To evaluate the impact of item replacement on system performance and operational efficiency.
  • To investigate the influence of multi-component demand on customer arrivals and system dynamics.

Main Methods:

  • Formulation of a level-dependent quasi-birth-and-death process.
  • Computation of steady-state probabilities using Neuts and Rao's truncation method.
  • Derivation of system stability conditions and performance measures (e.g., expected cost, number of items, customers).

Main Results:

  • The system with item replacement demonstrates superior efficiency compared to a non-replacement model.
  • Multi-component demand significantly boosts customer arrival rates.
  • Parametric sensitivity analysis quantifies the impact of various factors on total cost and system congestion.

Conclusions:

  • Implementing a strategic replacement policy is crucial for optimizing two-commodity queueing-inventory systems.
  • Understanding the interplay between demand patterns and inventory management is key to profitability.
  • The developed model provides valuable insights for managing complex commercial inventory systems.