IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v39y1992i5p599-611.html
   My bibliography  Save this article

Isotonic median regression for orders representable by rooted trees

Author

Listed:
  • Nilotpal Chakravarti

Abstract

The isotonic median regression problem arising in statistics is as follows. We are given m observations falling into n sets, the ith set containing mi observations. The problem requires the determination of n real numbers, the ith being the value “fitted” to each observation in the ith set. These n numbers chosen must satisfy certain (total or partial) order requirements and minimize the distance between the vectors of observed and fitted values in the l1 norm. We present a simple algorithm, of time complexity O(mn), for calculating isotonic median regression for orders representable by rooted trees. We believe that this algorithm is the best currently available for this problem. The algorithm is validated by a linear programming approach which provides additional insight.

Suggested Citation

  • Nilotpal Chakravarti, 1992. "Isotonic median regression for orders representable by rooted trees," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(5), pages 599-611, August.
    • Handle: RePEc:wly:navres:v:39:y:1992:i:5:p:599-611
    DOI: 10.1002/1520-6750(199208)39:53.0.CO;2-#
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(199208)39:53.0.CO;2-#
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(199208)39:53.0.CO;2-#?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. Menendez, J. A. & Salvador, B., 1987. "An algorithm for isotonic median regression," Computational Statistics & Data Analysis, Elsevier, vol. 5(4), pages 399-406, September.
    2. Ming S. Hung, 1983. "Technical Note—A Polynomial Simplex Method for the Assignment Problem," Operations Research, INFORMS, vol. 31(3), pages 595-600, June.
    3. William L. Maxwell & John A. Muckstadt, 1985. "Establishing Consistent and Realistic Reorder Intervals in Production-Distribution Systems," Operations Research, INFORMS, vol. 33(6), pages 1316-1341, December.
    4. Nilotpal Chakravarti, 1989. "Isotonic Median Regression: A Linear Programming Approach," Mathematics of Operations Research, INFORMS, vol. 14(2), pages 303-308, May.
    5. Robin Roundy, 1986. "A 98%-Effective Lot-Sizing Rule for a Multi-Product, Multi-Stage Production / Inventory System," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 699-727, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Ravindra K. Ahuja & James B. Orlin, 2001. "A Fast Scaling Algorithm for Minimizing Separable Convex Functions Subject to Chain Constraints," Operations Research, INFORMS, vol. 49(5), pages 784-789, October.

    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. Ravindra K. Ahuja & James B. Orlin, 2001. "A Fast Scaling Algorithm for Minimizing Separable Convex Functions Subject to Chain Constraints," Operations Research, INFORMS, vol. 49(5), pages 784-789, October.
    2. Adeinat, Hamza & Pazhani, Subramanian & Mendoza, Abraham & Ventura, Jose A., 2022. "Coordination of pricing and inventory replenishment decisions in a supply chain with multiple geographically dispersed retailers," International Journal of Production Economics, Elsevier, vol. 248(C).
    3. Chung-Piaw Teo & Dimitris Bertsimas, 2001. "Multistage Lot Sizing Problems via Randomized Rounding," Operations Research, INFORMS, vol. 49(4), pages 599-608, August.
    4. Li, Xiuhui & Wang, Qinan, 2007. "Coordination mechanisms of supply chain systems," European Journal of Operational Research, Elsevier, vol. 179(1), pages 1-16, May.
    5. Julien Bramel & Shobhna Goyal & Paul Zipkin, 2000. "Coordination of Production/Distribution Networks with Unbalanced Leadtimes," Operations Research, INFORMS, vol. 48(4), pages 570-577, August.
    6. Shiman Ding & Philip M. Kaminsky, 2020. "Centralized and Decentralized Warehouse Logistics Collaboration," Manufacturing & Service Operations Management, INFORMS, vol. 22(4), pages 812-831, July.
    7. Mendoza, Abraham & Ventura, José A., 2010. "A serial inventory system with supplier selection and order quantity allocation," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1304-1315, December.
    8. Ahuja, Ravindra K., 1956- & Orlin, James B., 1953-, 1997. "Solving the convex ordered set problem," Working papers WP 3988-97., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    9. Boissiere, J. & Frein, Y. & Rapine, C., 2008. "Optimal stationary policies in a 3-stage serial production-distribution logistic chain facing constant and continuous demand," European Journal of Operational Research, Elsevier, vol. 186(2), pages 608-619, April.
    10. Kevin H. Shang & Jing-Sheng Song & Paul H. Zipkin, 2009. "Coordination Mechanisms in Decentralized Serial Inventory Systems with Batch Ordering," Management Science, INFORMS, vol. 55(4), pages 685-695, April.
    11. Luca Bertazzi & Maria Grazia Speranza, 1999. "Minimizing logistic costs in multistage supply chains," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(4), pages 399-417, June.
    12. Garren Steven T., 2003. "Improved estimation of medians subject to order restrictions in unimodal symmetric families," Statistics & Risk Modeling, De Gruyter, vol. 21(4/2003), pages 367-380, April.
    13. Herer, Yale T., 1999. "Submodularity and the traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 114(3), pages 489-508, May.
    14. Luca Bertazzi & Maria Grazia Speranza & Walter Ukovich, 2000. "Exact and Heuristic Solutions for a Shipment Problem with Given Frequencies," Management Science, INFORMS, vol. 46(7), pages 973-988, July.
    15. Bertazzi, Luca & Grazia Speranza, Maria, 2005. "Worst-case analysis of the full load policy in the single link problem," International Journal of Production Economics, Elsevier, vol. 93(1), pages 217-224, January.
    16. Chu, Chi-Leung & Leon, V. Jorge, 2008. "Power-of-two single-warehouse multi-buyer inventory coordination with private information," International Journal of Production Economics, Elsevier, vol. 111(2), pages 562-574, February.
    17. Mark Goh & Ou Jihong & Teo Chung‐Piaw, 2001. "Warehouse sizing to minimize inventory and storage costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(4), pages 299-312, June.
    18. Mili Mehrotra & Milind Dawande & Srinagesh Gavirneni & Mehmet Demirci & Sridhar Tayur, 2011. "OR PRACTICE---Production Planning with Patterns: A Problem from Processed Food Manufacturing," Operations Research, INFORMS, vol. 59(2), pages 267-282, April.
    19. Vroblefski, Mark & Ramesh, R. & Zionts, Stanley, 2000. "Efficient lot-sizing under a differential transportation cost structure for serially distributed warehouses," European Journal of Operational Research, Elsevier, vol. 127(3), pages 574-593, December.
    20. Brian Q. Rieksts & José A. Ventura & Yale T. Herer & Daning Sun, 2007. "Technical note: Worst‐case performance of power‐of‐two policies for serial inventory systems with incremental quantity discounts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 583-587, August.

    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:39:y:1992:i:5:p:599-611. 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.