Skip to main content
SpringerLink
Log in

On the newsboy model with a cutoff transaction size

  • Published:
IIE Transactions

Abstract

In this paper we analyse the effect of a cutoff transaction size on the average inventory cost in a simple newsboy setting. It is assumed that customers with an order larger than a prespecified cutoff transaction size are satisfied in an alternative way, against additional cost. For compound Poisson demand with discrete order sizes, we show how to determine the average cost and an optimal cutoff transaction size. Because the computational effort to calculate the exact cost is quite large, we also consider an approximate model. By approximating the distribution of the total demand during a period by the normal distribution one can determine an expression for the average cost function that solely depends on the cutoff transaction size. A significant advantage of this approximation is that we can solve problems of any size. The quality of using the normal approximation is evaluated through a number of numerical experiments, which show that the approximate results are satisfactory.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Silver, E.A. (1970) Some ideas related to the inventory control of items having erratic demand patterns. Journal of the Canadian Operations Research Society, 8, 87-100.

    Google Scholar 

  2. Hollier, R.H., Mak, K.L. and Lam, C.L. (1995) Continuous review (s, S) policies for inventory systems incorporating a cutoff transaction size. International Journal of Production Research, 33, 2855-2865.

    Google Scholar 

  3. Krever, M. (1996) L.I.M.S.: logistics inventory management system. Technical Report v96.1, CERN Laboratory, Geneva, Switzerland.

    Google Scholar 

  4. Nass, R., Dekker, R. and van Sonderen-Huisman, W. (1997) Distribution management by means of cutoff order size: a case study. Journal of the Operational Research Society, 48, 1057-1064.

    Google Scholar 

  5. Lee, H.L. and Nahmias, S. (1993) Single-product, single-location models. in Handbooks in OR & MS, vol. 4, Logistics of production and inventory, Graves, S.C., Rinnooy Kan, A.H.G. and Zipkin, P. (eds), Elsevier Science Publishers, Amsterdam, pp 3-55.

    Google Scholar 

  6. Porteus, E.L. (1990) Stochastic inventory theory. in Handbooks in OR & MS, Vol. 2, Stochastic models, Heyman, D.P. and Sobel, M.J. (eds), Elsevier Science Publishers, Amsterdam, pp 605-652.

    Google Scholar 

  7. Ballou, R.H. (1992) Business Logistics Management, 3rd ed,. Prentice Hall, Englewood Cliffs, NJ. p. 43.

    Google Scholar 

  8. Popp, W. (1965) Simple and combined inventory policies, production to stock or to order? Management Science, 11, 868-873.

    Google Scholar 

  9. Magee, J.F. and Boodman, D.M. (1967) Production Planning and Inventory Control, 2nd ed, McGraw-Hill, New York.

    Google Scholar 

  10. Hollier, R.H., Mak, K.L. and Lam, C.L. (1995) An inventory model for items with demands satisfied from stock or by special deliveries. International Journal of Production Economics, 42, 229-236.

    Google Scholar 

  11. Mak, K.L. and Lai, K.K. (1995) The determination of optimal partial fill policy for an inventory system with lumpy demand items. Applied Mathematical Modelling, 19, 724-737.

    Google Scholar 

  12. Mak, K.L. and Lai, K.K. (1995) Optimal (s, S) policy for an inventory system when the demand can be partially satisfied. International Journal of Systems Science, 26, 213-231.

    Google Scholar 

  13. Adelson, R.M. (1966) Compound Poisson distributions. Operations Research Quarterly, 17, 73-75.

    Google Scholar 

  14. Zheng, Y.-S. and Federgruen, A. (1991) Finding optimal (s, S) policies is about as simple as evaluating a single policy. Operations Research, 39, 654-665.

    Google Scholar 

  15. Kleijn, M.J. and Dekker, R. (1998) Using break quantities for tactical optimisation in multi-stage distribution systems, in Advances in Distribution Logistics, Fleischmann, B., van Nunen, J.A.E.E., Grazia Speranza, M. and Stähly, P. (eds), Springer-Verlag, Berlin-Heidelberg, pp 305-318.

    Google Scholar 

  16. Tijms, H.C. (1994) Stochastic Models: An Algorithmic Approach. Wiley, New York.

    Google Scholar 

  17. Tyworth, J.E. and O'Neill, L. (1997) Robustness of the normal approximation of lead-time demand in a distribution setting. Naval Research Logistics, 44, 165-186.

    Google Scholar 

  18. Silver, E.A. and Peterson, R. (1985) Decision Systems for Inventory Management and Production Planning, John Wiley & Sons, New York.

    Google Scholar 

  19. Dekker, R., Kleijn, M.J. and de Kok, A.G. (1998) The break quantity rule's effect on inventory costs in a 1-warehouse, N-retailers distribution system. International Journal of Production Economics, 56-57, 61-68.

    Google Scholar 

  20. Topkis, D.M. (1968) Optimal ordering and rationing policies in a nonstationary dynamic inventory model with n demand classes. Management Science, 15, 160-176.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands

    R. Dekker

  2. Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands

    J.B.G. Frenk

  3. Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands

    M.J. Kleijn

  4. Department of Technology Management, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    A.G. de Kok

Authors
  1. R. Dekker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J.B.G. Frenk
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M.J. Kleijn
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A.G. de Kok
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dekker, R., Frenk, J., Kleijn, M. et al. On the newsboy model with a cutoff transaction size. IIE Transactions 32, 461–469 (2000). https://doi.org/10.1023/A:1007649027857

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007649027857

Keywords

Search

Navigation