IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v36y1989i4p463-477.html
   My bibliography  Save this article

Estimating the lead‐time demand distribution for an autocorrelated demand by the pearson system and a normal approximation

Author

Listed:
  • Bong‐Geun An
  • Stergios B. Fotopoulos
  • Min‐Chiang Wang

Abstract

The exact first four moments of lead‐time demand L are derived for an AR(1) and a MA(1) demand structures where the arbitrary lead‐time distribution is assumed to be independent of the demand structure. These moments then form a basis for the Pearson curve‐fitting procedure for estimating the distribution of L. A normal approximation to L, a version of the central limit theorem, is obtained under some general conditions. Reorder points (ROPs) of an inventory system are then estimated based on the Pearson system and a normal approximation. Their performances are evaluated. Numerical investigation shows that the Pearson system performs extremely well. The normal approximation, however, is good only for some limited cases, and is sensitive to the choice of the lead‐time distribution. A possible improvement is noted.

Suggested Citation

  • Bong‐Geun An & Stergios B. Fotopoulos & Min‐Chiang Wang, 1989. "Estimating the lead‐time demand distribution for an autocorrelated demand by the pearson system and a normal approximation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(4), pages 463-477, August.
    • Handle: RePEc:wly:navres:v:36:y:1989:i:4:p:463-477
    DOI: 10.1002/1520-6750(198908)36:43.0.CO;2-R
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(198908)36:43.0.CO;2-R
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(198908)36:43.0.CO;2-R?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. J. K. Ord & U. Bagchi, 1983. "The truncated normal–gamma mixture as a distribution for lead time demand," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 30(2), pages 359-365, June.
    2. Uttarayan Bagchi, 1987. "Modeling lead‐time demand for lumpy demand and variable lead time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 687-704, October.
    3. C. S. Davis & M. A. Stephens, 1983. "Approximate Percentage Points Using Pearson Curves," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(3), pages 322-327, November.
    4. Fotopoulos, Stergios & Wang, Min-Chiang & Rao, S. Subba, 1988. "Safety stock determination with correlated demands and arbitrary lead times," European Journal of Operational Research, Elsevier, vol. 35(2), pages 172-181, May.
    5. Chandrasekhar Das, 1976. "Explicit formulas for the order size and reorder point in certain inventory problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(1), pages 25-30, March.
    6. Wang, Min-Chiang, 1987. "Estimating the lead-time demand distribution when the daily demand is non-normal and autocorrelated Hon-Shiang LAU," European Journal of Operational Research, Elsevier, vol. 29(1), pages 60-69, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Urban, Timothy L., 2005. "A periodic-review model with serially-correlated, inventory-level-dependent demand," International Journal of Production Economics, Elsevier, vol. 95(3), pages 287-295, March.
    2. Altay, Nezih & Litteral, Lewis A. & Rudisill, Frank, 2012. "Effects of correlation on intermittent demand forecasting and stock control," International Journal of Production Economics, Elsevier, vol. 135(1), pages 275-283.
    3. Takashi Shinzato, 2017. "Property Safety Stock Policy for Correlated Commodities Based on Probability Inequality," Papers 1701.02245, arXiv.org.
    4. Xiang, Mengyuan & Rossi, Roberto & Martin-Barragan, Belen & Tarim, S. Armagan, 2023. "A mathematical programming-based solution method for the nonstationary inventory problem under correlated demand," European Journal of Operational Research, Elsevier, vol. 304(2), pages 515-524.
    5. Janssen, F.B.S.L.P. & Heuts, R.M.J. & de Kok, T., 1996. "The Value of Information in an (R,s,Q) Inventory Model," Other publications TiSEM 4b589d1f-2822-4c0f-9dea-6, Tilburg University, School of Economics and Management.
    6. Halkos, George & Kevork, Ilias, 2013. "Forecasting the optimal order quantity in the newsvendor model under a correlated demand," MPRA Paper 44189, University Library of Munich, Germany.
    7. Janssen, F.B.S.L.P. & Heuts, R.M.J. & de Kok, T., 1996. "The Value of Information in an (R,s,Q) Inventory Model," Discussion Paper 1996-21, Tilburg University, Center for Economic Research.
    8. Amar Sapra & Van-Anh Truong & Rachel Q. Zhang, 2010. "How Much Demand Should Be Fulfilled?," Operations Research, INFORMS, vol. 58(3), pages 719-733, June.
    9. Z S Hua & B Zhang & J Yang & D S Tan, 2007. "A new approach of forecasting intermittent demand for spare parts inventories in the process industries," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(1), pages 52-61, January.
    10. Layth C. Alwan & Christian H. Weiß, 2017. "INAR implementation of newsvendor model for serially dependent demand counts," International Journal of Production Research, Taylor & Francis Journals, vol. 55(4), pages 1085-1099, February.
    11. Richard A. Grimlund, 1990. "Combined monetary unit sampling from several independent populations: Sample size planning and sample evaluation with the moment method," Contemporary Accounting Research, John Wiley & Sons, vol. 6(2), pages 446-484, March.
    12. Mahmut Parlar & Defne Berkin, 1991. "Future supply uncertainty in EOQ models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(1), pages 107-121, February.
    13. Mahdavi, Mojtaba & Olsen, Tava Lennon, 2021. "The dual-serving problem: What is the right choice of inventory strategy?," Omega, Elsevier, vol. 103(C).
    14. Mekhtiev, Mirza Arif, 2013. "Analytical evaluation of lead-time demand in polytree supply chains with uncertain demand, lead-time and inter-demand time," International Journal of Production Economics, Elsevier, vol. 145(1), pages 304-317.
    15. repec:jss:jstsof:31:c02 is not listed on IDEAS
    16. Amílcar Oliveira & Teresa Oliveira & Antonio Seijas-Macías, 2018. "The uniform distribution product: an approach to the inventory model using R," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(2), pages 284-297, January.
    17. Gonçalves, João N.C. & Sameiro Carvalho, M. & Cortez, Paulo, 2020. "Operations research models and methods for safety stock determination: A review," Operations Research Perspectives, Elsevier, vol. 7(C).
    18. Lingxiu Dong & Hau L. Lee, 2003. "Optimal Policies and Approximations for a Serial Multiechelon Inventory System with Time-Correlated Demand," Operations Research, INFORMS, vol. 51(6), pages 969-980, December.
    19. Boute, Robert N. & Disney, Stephen M. & Lambrecht, Marc R. & Houdt, Benny Van, 2014. "Coordinating lead times and safety stocks under autocorrelated demand," European Journal of Operational Research, Elsevier, vol. 232(1), pages 52-63.
    20. Willemain, Thomas R. & Smart, Charles N. & Schwarz, Henry F., 2004. "A new approach to forecasting intermittent demand for service parts inventories," International Journal of Forecasting, Elsevier, vol. 20(3), pages 375-387.
    21. Tee, Yeu-San & Rossetti, Manuel D., 2002. "A robustness study of a multi-echelon inventory model via simulation," International Journal of Production Economics, Elsevier, vol. 80(3), pages 265-277, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:navres:v:36:y:1989:i:4:p:463-477. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.