IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v78y2024i1p228-243.html
   My bibliography  Save this article

Joint probabilities under expected value constraints, transportation problems, maximum entropy in the mean

Author

Listed:
  • Henryk Gzyl
  • Silvia Mayoral

Abstract

Here we consider an application of the method of maximum entropy in the mean to solve an extension of the problem of finding a discrete probability distribution from the knowledge of its marginals. The extension consists of determining joint probabilities when, besides specifying the marginals, we specify the expected value of some given random variables. The proposed method can incorporate constraints as the the requirement that the joint probabilities have to fall within known ranges. To motivate, think of the marginal probabilities as demands or supplies, and of the joint probability as the fraction of the supplies to be shipped from the production sites to the demand sites, thus joint probabilities become transportation policies. Fixing the cost of a transportation policy is equivalent to requiring that the unknown probability yields a given value to some random variable, and prescribing the range for each unknown may have an economical interpretation.

Suggested Citation

  • Henryk Gzyl & Silvia Mayoral, 2024. "Joint probabilities under expected value constraints, transportation problems, maximum entropy in the mean," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 78(1), pages 228-243, February.
    • Handle: RePEc:bla:stanee:v:78:y:2024:i:1:p:228-243
    DOI: 10.1111/stan.12314
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/stan.12314
    Download Restriction: no
    File URL: https://libkey.io/10.1111/stan.12314?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. Costis Maglaras & Serkan Eren, 2015. "A Maximum Entropy Joint Demand Estimation and Capacity Control Policy," Production and Operations Management, Production and Operations Management Society, vol. 24(3), pages 438-450, March.
    2. Hern'an Larralde, 2012. "Maximum Entropy distributions of correlated variables with prespecified marginals," Papers 1212.0440, arXiv.org.
    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. Cong Shi & Weidong Chen & Izak Duenyas, 2016. "Technical Note—Nonparametric Data-Driven Algorithms for Multiproduct Inventory Systems with Censored Demand," Operations Research, INFORMS, vol. 64(2), pages 362-370, April.
    2. Boxiao Chen & Xiuli Chao & Cong Shi, 2021. "Nonparametric Learning Algorithms for Joint Pricing and Inventory Control with Lost Sales and Censored Demand," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 726-756, May.
    3. Zizhuo Wang & Chaolin Yang & Hongsong Yuan & Yaowu Zhang, 2021. "Aggregation Bias in Estimating Log‐Log Demand Function," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 3906-3922, November.
    4. Gönsch, Jochen, 2017. "A survey on risk-averse and robust revenue management," European Journal of Operational Research, Elsevier, vol. 263(2), pages 337-348.
    5. Jiri Chod & Mihalis G. Markakis & Nikolaos Trichakis, 2021. "On the Learning Benefits of Resource Flexibility," Management Science, INFORMS, vol. 67(10), pages 6513-6528, October.
    6. Fleischhacker, Adam J. & Fok, Pak-Wing, 2015. "On the relationship between entropy, demand uncertainty, and expected loss," European Journal of Operational Research, Elsevier, vol. 245(2), pages 623-628.
    7. Tianyang Wang & James S. Dyer & John C. Butler, 2016. "Modeling Correlated Discrete Uncertainties in Event Trees with Copulas," Risk Analysis, John Wiley & Sons, vol. 36(2), pages 396-410, February.
    8. Soroush Saghafian & Brian Tomlin, 2016. "The Newsvendor under Demand Ambiguity: Combining Data with Moment and Tail Information," Operations Research, INFORMS, vol. 64(1), pages 167-185, February.

    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:bla:stanee:v:78:y:2024:i:1:p:228-243. 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: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    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.