Skip to main content
Log in

An (r, nQ) inventory model for packaged deteriorating products with compound Poisson demand

  • General Paper
  • Published:
Journal of the Operational Research Society

Abstract

We consider a liquid type of a deteriorating item which is packaged by an outside supplier and is delivered to final customers by a distributor. Customers arrive according to a Poisson process and ask for an integer number of packages. Unsatisfied demands are backordered. The inventory is reviewed continuously and replenished from an external supplier with a positive deterministic lead time following an (r, nQ) policy. The product in each package deteriorates continuously over time during transportation and storage. Therefore, the distributor cannot deliver exactly one unit of usable material in each package. We develop a model to determine the optimal inventory control parameters and the required size of a package to minimize expected average costs and illustrate the benefit of this method compared to a sequential approach based on an example from practice.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1

Similar content being viewed by others

References

  • Axsäter S (2006). Inventory Control. 2nd edn, Springer: New York.

    Google Scholar 

  • de Kok T, Pyke D and Baganha M (1996). The undershoot of the reorder-level in an (s,nQ) model and its relation to the replenishment order size distribution. Technical report, Eindhoven University of Technology.

  • Ghare P and Schrader G (1963). A model for exponentially decaying inventory. Journal of Industrial Engineering 14: 238–243.

    Google Scholar 

  • Goyal SK and Giri BC (2001). Recent trends in modeling of deteriorating inventory. European Journal of Operational Research 134: 1–16.

    Article  Google Scholar 

  • Hadley G and Whitin T (1963). Analysis of Inventory Systems. Prentice-Hall: Englewood Cliffs, NJ.

    Google Scholar 

  • Kalpakam S and Arivarignan G (1988). A continuous review perishable inventory model. Journal of Statistics 19 (3): 389–398.

    Article  Google Scholar 

  • Kalpakam S and Sapna KP (1994). Continuous review (s, S) inventory system with random lifetimes and positive leadtimes. Operations Research Letters 16: 115–119.

    Article  Google Scholar 

  • Kalpakam S and Shanthi S (2000). A perishable system with modified base stock policy and random supply quantity. Computers and Mathematics with Applications 39: 79–89.

    Article  Google Scholar 

  • Karaesmen I, Scheller-Wolf A and Deniz B (2011). Managing perishable and aging inventories: Review and future research directions. In: Kempf K, Keskinocak P and Uzsoy P (eds). Planning Production and Inventories in the Extended Enterprise—A State-of-the-Art Handbook. Vol. 151, International Series in Operations Research and Management Science Springer: New York, pp 393–436.

    Chapter  Google Scholar 

  • Li R, Lan H and Mawhinney JR (2010). A review on deteriorating inventory study. Journal of Service Science & Management 3: 117–129.

    Article  Google Scholar 

  • Lin C and Lin Y (2007). A cooperative inventory policy with deteriorating items, for a two-echelon model. European Journal of Operational Research 178: 92–111.

    Article  Google Scholar 

  • Liu L and Yang T (1999). An (s, S) random lifetime inventory model with a positive lead time. European Journal of Operational Research 113: 52–63.

    Article  Google Scholar 

  • Molana SMH and Davoudpour H (2010). A modified (S−1, S) inventory system for deteriorating items under demand uncertainty. Working paper.

  • Nahmias S (1982). Perishable inventory theory: A review. Operations Research 30 (4): 680–708.

    Article  Google Scholar 

  • Nahmias S and Wang S (1979). A heuristic lot-size reorder point model for decaying inventories. Management Science 25: 90–97.

    Article  Google Scholar 

  • Olsson F (2010). Modelling two-echelon serial inventory systems with perishable items. IMA Journal of Management Mathematics 21: 1–17.

    Article  Google Scholar 

  • Raafat F (1991). Survey of literature on continuously deteriorating inventory models. Journal of the Operational Research Society 42 (1): 27–37.

    Article  Google Scholar 

  • Wee HM (1993). Economic production lot size model for deteriorating items with partial backordering. Computers in Industrial Engineering 24: 449–458.

    Article  Google Scholar 

  • Yano CA and Lee HL (1995). Lot sizing with random yields: A review. Operations Research 43 (2): 311–334.

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the helpful comments of two anonymous reviewers. This research was conducted while the first author was a visiting Ph.D. student at the University of Vienna.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S Minner.

Appendix

Appendix

In Model 2, α is a continuous decision variable and we investigate the convexity of C{α, r, Q) according to α for given r and Q.

For the penalty cost Cp, t B depends on α

We also know

According to C P from (15) the first derivative of C P is

We conclude that:

The second derivative is

Using , expression (A.2) becomes

It is obvious that expression (A.3) is positive, so C(α, r, Q) is convex in α for any given r and Q.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Molana, S., Davoudpour, H. & Minner, S. An (r, nQ) inventory model for packaged deteriorating products with compound Poisson demand. J Oper Res Soc 63, 1499–1507 (2012). https://doi.org/10.1057/jors.2011.154

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1057/jors.2011.154

Keywords

Navigation