pp 1–15 | Cite as

Continuous review (s, Q) inventory system with random lifetime and two demand classes

  • Umay Uzunoglu KocerEmail author
  • Bahar Yalcin
Theoretical Article


This paper examines a continuous review inventory model for perishable items with two demand classes. Demands for both classes occur according to Poisson process. The items in inventory are perishable products and have exponential lifetimes. The time after placing an order is an exponential random variable. When the on-hand inventory drops to pre-specified level s, only the priority customer demands are met whereas the demands from ordinary customers are lost. And also, the demand occurring stock-out periods are lost. The inventory system is characterized by continuous-time Markov process and steady-state probabilities are derived. The expected cost function is formulated and a numerical study is provided for optimization.


Markov process Perishable inventory Two demand classes Random lifetime Random lead time 



We would like to thank the anonymous referees who have improved our work with their invaluable comments.


  1. 1.
    Escalona, P., Ordóñez, F., Kauak, I.: Critical level rationing in inventory systems with continuously distributed demand. OR Spectr. 39, 273–301 (2017). CrossRefGoogle Scholar
  2. 2.
    Gürler, Ü., Özkaya, B.Y.: Analysis of the (s, S) policy for perishables with a random lifetime. IIE Trans. 40, 759–781 (2008)CrossRefGoogle Scholar
  3. 3.
    Haijema, R., Van der Wal, J., Van Dijk, N.M.: Blood platelet production: a multi-type perishable inventory problem. In: Fleuren, H., den Hertog, D., Kort, P. (eds.) Operations Research Proceedings. Springer, Berlin (2005)Google Scholar
  4. 4.
    Haijema, R.: A new class of stock-level dependent ordering policies for perishables with a short maximum shelf life. Int. J. Prod. Econ. 143, 434–439 (2013)CrossRefGoogle Scholar
  5. 5.
    Isotupa, K.P.S.: An (s, Q) Markovian inventory system with lost sales and two demand classes. Math. Comput. Model. 43, 687–694 (2006)CrossRefGoogle Scholar
  6. 6.
    Isotupa, S.: Cost analysis of an (S - 1, S) inventory system with two demand classes and rationing. Ann. Oper. Res. 233, 411–421 (2015). CrossRefGoogle Scholar
  7. 7.
    Jeganathan, K., Kathiresan, J., Anbazhagan, N.: A retrial inventory system with priority customers and second optional service. Opsearch 53, 808–834 (2016). CrossRefGoogle Scholar
  8. 8.
    Kalpakam, S., Arivarignan, G.: A continuous review perishable inventory model. Statistics 19, 389–398 (1988)CrossRefGoogle Scholar
  9. 9.
    Kalpakam, S., Sapna, K.P.: Continuous review (s, S) inventory system with random lifetimes and positive lead times. Oper. Res. Lett. 16, 115–119 (1994)CrossRefGoogle Scholar
  10. 10.
    Kalpakam, S., Shanti, S.: A continuous review perishable system with renewal demands. Ann. Oper. Res. 143, 211–225 (2006)CrossRefGoogle Scholar
  11. 11.
    Kaspi, H., Perry, D.: Inventory systems of perishable commodities. Adv. Appl. Probab. 15, 674–685 (1983)CrossRefGoogle Scholar
  12. 12.
    Kleijn, M.J., Dekker, R.: An overview of inventory systems with several demand classes. In: Speranza, M.G., Stähly, P. (eds.) New Trends in Distribution Logistics. Lecture Notes in Economics and Mathematical Systems, vol. 480. Springer, Berlin (1999)Google Scholar
  13. 13.
    Lian, Z., Liu, X., Zhao, N.: A perishable inventory model with Markovian renewal demands. Int. J. Prod. Econ. 121, 176–182 (2009)CrossRefGoogle Scholar
  14. 14.
    Liu, L.: (s, S) Continuous review models for inventory with random lifetimes. Oper. Res. Lett. 9, 161–167 (1990)CrossRefGoogle Scholar
  15. 15.
    Liu, L., Lian, Z.: (s, S) Continuous review models for products with fixed lifetimes. Oper. Res. 47(1), 150–158 (1999)CrossRefGoogle Scholar
  16. 16.
    Liu, L., Shi, D.H.: An (s, S) model for inventory with exponential lifetimes and renewal demands. Nav. Res. Logist. 46(1), 39–56 (1999)CrossRefGoogle Scholar
  17. 17.
    Liu, M., Feng, M., Wong, C.Y.: Flexible service policies for Markov inventory system with two demand classes. Int. J. Prod. Econ. 151, 180–185 (2014)CrossRefGoogle Scholar
  18. 18.
    Melchiors, P., Dekker, R., Kleijn, M.J.: Inventory rationing in an (s, Q) inventory model with lost sales and two demand classes. J. Oper. Res. Soc. 51(1), 111–122 (2000)CrossRefGoogle Scholar
  19. 19.
    Moon, I., Kang, S.: Rationing policies for some inventory systems. J. Oper. Res. Soc. 49(5), 509–518 (1998)CrossRefGoogle Scholar
  20. 20.
    Nahmias, S., Demmy, W.S.: Operating characteristics of an inventory system with rationing. Manag. Sci. 27(11), 1236–1245 (1981)CrossRefGoogle Scholar
  21. 21.
    Ravichandran, N.: Probabilistic analysis of a continuous review perishable inventory system. OR Spektrum 10, 23–27 (1988)CrossRefGoogle Scholar
  22. 22.
    Ravichandran, N.: Stochastic analysis of a continuous review perishable inventory system with positive lead time and Poisson demand. Eur. J. Oper. Res. 84, 444–457 (1995)CrossRefGoogle Scholar
  23. 23.
    Saranya, N., Lawrence, A.S.: A stochastic inventory system with replacement of perishable items. Opsearch 56, 563–582 (2019). CrossRefGoogle Scholar
  24. 24.
    Tiwari, S., Daryanto, Y., Wee, H.M.: Sustainable inventory management with deteriorating and imperfect quality items considering carbon emission. J. Clean. Prod. 192, 281–292 (2018)CrossRefGoogle Scholar
  25. 25.
    Veinott, A.F.: Optimal policy in a dynamic, single product, nonstationary inventory model with several demand classes. Oper. Res. 13(5), 761–778 (1965)CrossRefGoogle Scholar
  26. 26.
    Vrat, P., Gupta, R., Bhatnagar, A., Pathak, D.K., Fulzele, V.: Literature review analytics (LRA) on sustainable cold-chain for perishable food products: research trends and future directions. Opsearch 55, 601–627 (2018). CrossRefGoogle Scholar
  27. 27.
    Williams, C.L., Pattuwo, B.E.: A perishable inventory model with positive order lead times. Eur. J. Oper. Res. 116, 352–373 (1999)CrossRefGoogle Scholar
  28. 28.
    Zhao, N., Lian, Z.: A queuing-inventory system with two classes of customers. Int. J. Prod. Econ. 129, 225–231 (2011)CrossRefGoogle Scholar

Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  1. 1.Department of Statistics, Faculty of ScienceDokuz Eylul UniversityIzmirTurkey

Personalised recommendations