IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v84y2022i1d10.1007_s10898-022-01131-5.html
   My bibliography  Save this article

Fractional 0–1 programming and submodularity

Author

Listed:
  • Shaoning Han

    (University of Southern California)

  • Andrés Gómez

    (University of Southern California)

  • Oleg A. Prokopyev

    (University of Pittsburgh)

Abstract

In this note we study multiple-ratio fractional 0–1 programs, a broad class of $$\mathcal {NP}$$ NP -hard combinatorial optimization problems. In particular, under some relatively mild assumptions we provide a complete characterization of the conditions, which ensure that a single-ratio function is submodular. Then we illustrate our theoretical results with the assortment optimization and facility location problems, and discuss practical situations that guarantee submodularity in the considered application settings. In such cases, near-optimal solutions for multiple-ratio fractional 0–1 programs can be found via simple greedy algorithms.

Suggested Citation

  • Shaoning Han & Andrés Gómez & Oleg A. Prokopyev, 2022. "Fractional 0–1 programming and submodularity," Journal of Global Optimization, Springer, vol. 84(1), pages 77-93, September.
    • Handle: RePEc:spr:jglopt:v:84:y:2022:i:1:d:10.1007_s10898-022-01131-5
    DOI: 10.1007/s10898-022-01131-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-022-01131-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-022-01131-5?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Samyukta Sethuraman & Sergiy Butenko, 2015. "The maximum ratio clique problem," Computational Management Science, Springer, vol. 12(1), pages 197-218, January.
    2. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Laurent Alfandari & Alborz Hassanzadeh & Ivana Ljubić, 2021. "An Exact Method for Assortment Optimization under the Nested Logit Model," Working Papers hal-02463159, HAL.
    4. Amiri, Ali & Rolland, Erik & Barkhi, Reza, 1999. "Bandwidth packing with queuing delay costs: Bounding and heuristic solution procedures," European Journal of Operational Research, Elsevier, vol. 112(3), pages 635-645, February.
    5. Camilo Ortiz-Astorquiza & Ivan Contreras & Gilbert Laporte, 2017. "Formulations and Approximation Algorithms for Multilevel Uncapacitated Facility Location," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 767-779, November.
    6. Jacob Feldman & Huseyin Topaloglu, 2015. "Bounding Optimal Expected Revenues for Assortment Optimization under Mixtures of Multinomial Logits," Production and Operations Management, Production and Operations Management Society, vol. 24(10), pages 1598-1620, October.
    7. Céline Bonnet, 2001. "Assessing consumer response to Protected Designation of Origin labelling: a mixed multinomial logit approach," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 28(4), pages 433-450, December.
    8. Ljubić, Ivana & Moreno, Eduardo, 2018. "Outer approximation and submodular cuts for maximum capture facility location problems with random utilities," European Journal of Operational Research, Elsevier, vol. 266(1), pages 46-56.
    9. Paat Rusmevichientong & David Shmoys & Chaoxu Tong & Huseyin Topaloglu, 2014. "Assortment Optimization under the Multinomial Logit Model with Random Choice Parameters," Production and Operations Management, Production and Operations Management Society, vol. 23(11), pages 2023-2039, November.
    10. Alfandari, Laurent & Hassanzadeh, Alborz & Ljubić, Ivana, 2021. "An exact method for assortment optimization under the nested logit model," European Journal of Operational Research, Elsevier, vol. 291(3), pages 830-845.
    11. Kalyan Talluri & Garrett van Ryzin, 2004. "Revenue Management Under a General Discrete Choice Model of Consumer Behavior," Management Science, INFORMS, vol. 50(1), pages 15-33, January.
    12. K. Sridhar Moorthy & I. P. L. Png, 1992. "Market Segmentation, Cannibalization, and the Timing of Product Introductions," Management Science, INFORMS, vol. 38(3), pages 345-359, March.
    13. Paat Rusmevichientong & Zuo-Jun Max Shen & David B. Shmoys, 2010. "Dynamic Assortment Optimization with a Multinomial Logit Choice Model and Capacity Constraint," Operations Research, INFORMS, vol. 58(6), pages 1666-1680, December.
    14. Oleksii Ursulenko & Sergiy Butenko & Oleg Prokopyev, 2013. "A global optimization algorithm for solving the minimum multiple ratio spanning tree problem," Journal of Global Optimization, Springer, vol. 56(3), pages 1029-1043, July.
    15. Benati, Stefano & Hansen, Pierre, 2002. "The maximum capture problem with random utilities: Problem formulation and algorithms," European Journal of Operational Research, Elsevier, vol. 143(3), pages 518-530, December.
    16. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    18. Nimrod Megiddo, 1979. "Combinatorial Optimization with Rational Objective Functions," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 414-424, November.
    19. Shashi Mittal & Andreas S. Schulz, 2013. "A General Framework for Designing Approximation Schemes for Combinatorial Optimization Problems with Many Objectives Combined into One," Operations Research, INFORMS, vol. 61(2), pages 386-397, April.
    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. Kübra Tanınmış & Markus Sinnl, 2022. "A Branch-and-Cut Algorithm for Submodular Interdiction Games," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2634-2657, September.

    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. Dam, Tien Thanh & Ta, Thuy Anh & Mai, Tien, 2023. "Robust maximum capture facility location under random utility maximization models," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1128-1150.
    2. Dam, Tien Thanh & Ta, Thuy Anh & Mai, Tien, 2022. "Submodularity and local search approaches for maximum capture problems under generalized extreme value models," European Journal of Operational Research, Elsevier, vol. 300(3), pages 953-965.
    3. Julia Heger & Robert Klein, 2024. "Assortment optimization: a systematic literature review," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(4), pages 1099-1161, December.
    4. Méndez-Vogel, Gonzalo & Marianov, Vladimir & Lüer-Villagra, Armin, 2023. "The follower competitive facility location problem under the nested logit choice rule," European Journal of Operational Research, Elsevier, vol. 310(2), pages 834-846.
    5. Ngan Ha Duong & Tien Thanh Dam & Thuy Anh Ta & Tien Mai, 2022. "Joint Location and Cost Planning in Maximum Capture Facility Location under Multiplicative Random Utility Maximization," Papers 2205.07345, arXiv.org, revised Feb 2023.
    6. Çömez-Dolgan, Nagihan & Fescioglu-Unver, Nilgun & Cephe, Ecem & Şen, Alper, 2021. "Capacitated strategic assortment planning under explicit demand substitution," European Journal of Operational Research, Elsevier, vol. 294(3), pages 1120-1138.
    7. Kübra Tanınmış & Markus Sinnl, 2022. "A Branch-and-Cut Algorithm for Submodular Interdiction Games," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2634-2657, September.
    8. C. I. Chiang, 2023. "Availability control under online reviews in hospitality," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 22(5), pages 385-398, October.
    9. Mehrani, Saharnaz & Sefair, Jorge A., 2022. "Robust assortment optimization under sequential product unavailability," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1027-1043.
    10. Strauss, Arne K. & Klein, Robert & Steinhardt, Claudius, 2018. "A review of choice-based revenue management: Theory and methods," European Journal of Operational Research, Elsevier, vol. 271(2), pages 375-387.
    11. Flores, Alvaro & Berbeglia, Gerardo & Van Hentenryck, Pascal, 2019. "Assortment optimization under the Sequential Multinomial Logit Model," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1052-1064.
    12. Ruxian Wang & Zizhuo Wang, 2017. "Consumer Choice Models with Endogenous Network Effects," Management Science, INFORMS, vol. 63(11), pages 3944-3960, November.
    13. Antoine Désir & Vineet Goyal & Danny Segev & Chun Ye, 2020. "Constrained Assortment Optimization Under the Markov Chain–based Choice Model," Management Science, INFORMS, vol. 66(2), pages 698-721, February.
    14. Nan Liu & Yuhang Ma & Huseyin Topaloglu, 2020. "Assortment Optimization Under the Multinomial Logit Model with Sequential Offerings," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 835-853, July.
    15. Wang, Mengmeng & Zhang, Xun & Li, Xiaolong, 2023. "Multiple-purchase choice model: estimation and optimization," International Journal of Production Economics, Elsevier, vol. 265(C).
    16. Sumit Kunnumkal & Victor Martínez-de-Albéniz, 2019. "Tractable Approximations for Assortment Planning with Product Costs," Operations Research, INFORMS, vol. 67(2), pages 436-452, March.
    17. Ali Aouad & Vivek Farias & Retsef Levi, 2021. "Assortment Optimization Under Consider-Then-Choose Choice Models," Management Science, INFORMS, vol. 67(6), pages 3368-3386, June.
    18. Rui Chen & Hai Jiang, 2020. "Assortment optimization with position effects under the nested logit model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(1), pages 21-33, February.
    19. Ali Aouad & Danny Segev, 2021. "Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Preferences," Management Science, INFORMS, vol. 67(6), pages 3519-3550, June.
    20. Juan S. Borrero & Colin Gillen & Oleg A. Prokopyev, 2017. "Fractional 0–1 programming: applications and algorithms," Journal of Global Optimization, Springer, vol. 69(1), pages 255-282, September.

    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:spr:jglopt:v:84:y:2022:i:1:d:10.1007_s10898-022-01131-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.