IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v24y1976i4p718-725.html
   My bibliography  Save this article

On a General Solution of the Deterministic Lot Size Problem with Time-Proportional Demand

Author

Listed:
  • Michael Resh

    (Israel Ministry of Communications, Tel-Aviv, Israel)

  • Moshe Friedman

    (Arizona State University, Tempe, Arizona)

  • Lineu C. Barbosa

    (IBM Research Laboratory, San Jose, California)

Abstract

We reconsider the classical lot-size model with the assumption that demand rate is deterministic, starts at the origin, and linearly increases with time. Two relevant costs are involved: carrying cost and replenishment cost. The planning horizon is finite and known. The problem is to find the optimal schedule of replenishments, i.e., their number and the schedule of time intervals between consecutive orders. Mathematically, we have to find an integer m and the values of m continuous variables so as to minimize the total carrying and replenishments costs. We prove that for a givers number of replenishments m , there exists a unique vector of m time intervals that minimizes the total cost function. It is further shown that the total carrying cost obtained after substituting the optimal value of that vector is a convex function of m . The algorithm that determines the unique optimal value of m and the unique optimal scheduling of replenishments for m employs these mathematical results. Finally, we investigate the asymptotic properties of the model when the planning horizon is infinite.

Suggested Citation

  • Michael Resh & Moshe Friedman & Lineu C. Barbosa, 1976. "On a General Solution of the Deterministic Lot Size Problem with Time-Proportional Demand," Operations Research, INFORMS, vol. 24(4), pages 718-725, August.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:4:p:718-725
    DOI: 10.1287/opre.24.4.718
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.24.4.718
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.24.4.718?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Urban, Timothy L. & Baker, R. C., 1997. "Optimal ordering and pricing policies in a single-period environment with multivariate demand and markdowns," European Journal of Operational Research, Elsevier, vol. 103(3), pages 573-583, December.
    2. Balkhi, Zaid T., 2001. "On a finite horizon production lot size inventory model for deteriorating items: An optimal solution," European Journal of Operational Research, Elsevier, vol. 132(1), pages 210-223, July.
    3. Narayan Singh & Bindu Vaish & Shiv Ray Singh, 2014. "A collaborative strategy for a three echelon supply chain with ramp type demand, deterioration and inflation," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(3), pages 77-100.
    4. Sicilia, Joaquín & González-De-la-Rosa, Manuel & Febles-Acosta, Jaime & Alcaide-López-de-Pablo, David, 2014. "Optimal policy for an inventory system with power demand, backlogged shortages and production rate proportional to demand rate," International Journal of Production Economics, Elsevier, vol. 155(C), pages 163-171.
    5. Dye, Chung-Yuan & Chang, Horng-Jinh & Teng, Jinn-Tsair, 2006. "A deteriorating inventory model with time-varying demand and shortage-dependent partial backlogging," European Journal of Operational Research, Elsevier, vol. 172(2), pages 417-429, July.
    6. Hill, Roger M., 1996. "Batching policies for a product life cycle," International Journal of Production Economics, Elsevier, vol. 45(1-3), pages 421-427, August.
    7. Hung, Kuo-Chen, 2011. "An inventory model with generalized type demand, deterioration and backorder rates," European Journal of Operational Research, Elsevier, vol. 208(3), pages 239-242, February.
    8. Abbott, Harish & Palekar, Udatta S., 2008. "Retail replenishment models with display-space elastic demand," European Journal of Operational Research, Elsevier, vol. 186(2), pages 586-607, April.
    9. Hill, Roger M. & Omar, Mohd & Smith, David K., 1999. "Stock replenishment policies for a stochastic exponentially-declining demand process," European Journal of Operational Research, Elsevier, vol. 116(2), pages 374-388, July.
    10. Hong, Jae-Dong & Kim, Seung-Lae & Hayya, Jack C., 1996. "Dynamic setup reduction in production lot sizing with nonconstant deterministic demand," European Journal of Operational Research, Elsevier, vol. 90(1), pages 182-196, April.
    11. Konstantaras, Ioannis & Skouri, Konstantina & Benkherouf, Lakdere, 2021. "Optimizing inventory decisions for a closed–loop supply chain model under a carbon tax regulatory mechanism," International Journal of Production Economics, Elsevier, vol. 239(C).
    12. Chang, Horng-Jinh & Teng, Jinn-Tsair & Ouyang, Liang-Yuh & Dye, Chung-Yuan, 2006. "Retailer's optimal pricing and lot-sizing policies for deteriorating items with partial backlogging," European Journal of Operational Research, Elsevier, vol. 168(1), pages 51-64, January.
    13. Massonnet, G. & Gayon, J.-P. & Rapine, C., 2014. "Approximation algorithms for deterministic continuous-review inventory lot-sizing problems with time-varying demand," European Journal of Operational Research, Elsevier, vol. 234(3), pages 641-649.
    14. Yang, Hui-Ling & Teng, Jinn-Tsair & Chern, Maw-Sheng, 2002. "A forward recursive algorithm for inventory lot-size models with power-form demand and shortages," European Journal of Operational Research, Elsevier, vol. 137(2), pages 394-400, March.
    15. Skouri, K. & Konstantaras, I. & Papachristos, S. & Ganas, I., 2009. "Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate," European Journal of Operational Research, Elsevier, vol. 192(1), pages 79-92, January.
    16. Hill, Roger M., 1996. "Batching policies for linearly increasing demand with a finite input rate," International Journal of Production Economics, Elsevier, vol. 43(2-3), pages 149-154, June.

    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:inm:oropre:v:24:y:1976:i:4:p:718-725. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.