Advertisement

OPSEARCH

pp 1–20 | Cite as

A stochastic inventory system with replacement of perishable items

  • N. Saranya
  • A. Shophia LawrenceEmail author
Application Article

Abstract

This article presents a continuous review perishable inventory system in which the perished items will be replaced by the supplier at a later time. Demands occur according to a Markov arrival process. The items in the inventory have exponential life times and these perished items are stored in a place, called pool for replacement. The (sS) ordering policy is adopted. At the time of placing an order, the ordering quantity is adjusted with number of items in the pool. The lead time is assumed to have phase type distribution. The joint probability distribution of the inventory level and the number of pooled items is obtained in the steady state case using the matrix-geometric methods. Various system performance measures in the steady state are derived and the total expected cost rate is calculated under a prefixed cost structure. The results derived in this work are numerically illustrated.

Keywords

Perishable inventory Replaceable items Markovian arrival process (s, S) ordering policy Phase type distribution 

Notes

Acknowledgements

The authors sincerely thank the editor and the anonymous reviewers for their useful comments and suggestions.

References

  1. 1.
    Amirthakodi, M., Sivakumar, B.: An inventory system with service facility and finite orbit size for feedback customers. Opsearch 52(2), 225–255 (2015)CrossRefGoogle Scholar
  2. 2.
    Bakker, M., Riezebos, J., Teunter, R.: Review of inventory systems with deterioration since 2001. Eur. J. Oper. Res. 221, 275–284 (2012)CrossRefGoogle Scholar
  3. 3.
    Goyal, S., Giri, B.: Recent trends in modeling of deteriorating inventory systems. Eur. J. Oper. Res. 34(1), 1–16 (2001)CrossRefGoogle Scholar
  4. 4.
    Gurler, U., Ozkaya, B.: A note on continuous review perishable inventory systems: models and heuristics. IIE Trans. 35, 321–323 (2003)CrossRefGoogle Scholar
  5. 5.
    Janssen, L., Claus, T., Sauer, J.: Literature review of deteriorating inventory models by key topics from 2012 to 2015. Int. J. Prod. Econ. 182, 86–112 (2016)CrossRefGoogle Scholar
  6. 6.
    Kalpakam, S., Sapna, : Continuous review \((s,{S})\) inventoy system with random lifetimes and positive lead times. Oper. Res. Lett. 16(2), 115–119 (1994)CrossRefGoogle Scholar
  7. 7.
    Karaesmen, I., Deiz, B., Scheller-Wolf, A.: Managing perishable and aging inventories: review and future research directions. In: Kempf, K., Keskinocak, P., Uzsoy, R. (eds. ) Kluwer International Series in Operations Research and Management Science, Advancing the State-of-the-art Subseries. Kluwer Academic Publishers (2008)Google Scholar
  8. 8.
    Lian, Z., Liu, L.: Continuous review perishable inventory systems: models and heuristics. IIE Trans. 33(9), 809–822 (2001)Google Scholar
  9. 9.
    Liu, L., Shi, D.: An \((s,{S})\) model for inventory with exponential lifetimes and renewal demands. Nav. Res. Logist. 46, 38–56 (1998)Google Scholar
  10. 10.
    Manuel, P., Shophia Lawrence, A., Arivarignan, G.: A stochastic perishable inventory system with random supply quantity. Int. J. Inf. Manag. Sci. 18(4), 317–334 (2007)Google Scholar
  11. 11.
    Manuel, P., Sivakumar, B., Arivarignan, G.: A perishable inventory system with service facilities and retrial customers. Comput. Ind. Eng. 54(3), 484–501 (2008)CrossRefGoogle Scholar
  12. 12.
    Nahmias, S.: Perishable inventory theory: a review. Oper. Res. 30, 680–708 (1982)CrossRefGoogle Scholar
  13. 13.
    Nahmias, S.: Perishable Inventory Systems. Springer, Berlin (2011)CrossRefGoogle Scholar
  14. 14.
    Neuts, M.: Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The Johns Hopkins University Press, Baltimore (1981)Google Scholar
  15. 15.
    Neuts, M.: Matrix-Analytic Methods on the Theory of Queues. CRC Press, Boca Raton (1995)Google Scholar
  16. 16.
    Padmavathi, I., Shophia Lawrence, A., Sivakumar, B.: A finite-source inventory system with postponed demands and modified \(m\) vacation policy. Opsearch 53(1), 41–62 (2016)CrossRefGoogle Scholar
  17. 17.
    Raafat, F.: A survey of lietrature on continuously deteriorating inventory models. J. Oper. Res. Soc. 42, 27–37 (1991)CrossRefGoogle Scholar
  18. 18.
    Radhamani, V., Sivakumar, B., Arivarignan, G.: An analysis of replenishment policies for perishable inventory system with postponed demand and multiple vacations. Int. J. Inventory Res. 3(3), 217–262 (2016)CrossRefGoogle Scholar
  19. 19.
    Ravichandran, N.: Stochastic analysis of a continuous review perishable inventory system with positive lead time and poisson demand. Eur. J. Oper. Res. 84(2), 444–457 (1995)CrossRefGoogle Scholar
  20. 20.
    Shah, N., Shah, Y.: Literature survey on inventory models for deteriorating items. Ekon. Anal. 44, 221–237 (2000)Google Scholar
  21. 21.
    Shophia Lawrence, A., Sivakumar, B., Arivarignan, G.: A perishable inventory system with service facility and finite source. Appl. Math. Model. 37, 4771–4786 (2013)CrossRefGoogle Scholar
  22. 22.
    Sivakumar, B.: A perishable inventory system with retrial demands and a finite population. J. Comput. Appl. Math. 224(1), 29–38 (2009)CrossRefGoogle Scholar
  23. 23.
    Sivakumar, B., Anbazhagan, N.: Stochastic inventory system with replaceable items. J. Comput. Optim. Econ. Financ. 2(3), 165–179 (2011)Google Scholar
  24. 24.
    Yadavalli, V.S.S., Sivakumar, B., Arivarignan, G., Olufeumi, A.: A multi server perishable inventory system with negative customers. Comput. Ind. Eng. 61, 254–273 (2011)CrossRefGoogle Scholar

Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  1. 1.Department of MathematicsMadurai Kamaraj UniversityMaduraiIndia

Personalised recommendations