IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v206y2010i1p144-154.html
   My bibliography  Save this article

Constrained group balancing: Why does it work

Author

Listed:
  • Krass, Dmitry
  • Ovchinnikov, Anton

Abstract

We consider a problem where a set of objects possessing multiple attributes must be partitioned into a certain number of groups so that the groups are as balanced as possible with respect to the number of objects possessing each attribute. This multi-criteria decision problem arises in a variety of practical applications, ranging from assigning students to study groups to designing level schedules for JIT assembly lines. A direct approach, enforcing balance through hard constraints, may lead to infeasibility, but works well in practice. We analyze this phenomenon from the worst-case and empirical perspectives, as well as through an in-depth analysis of one representative practical application - the design of student groups at the Rotman School of Management, University of Toronto. The goals of the analysis are to understand what classes of balancing problems may contain infeasible instances and how prevalent such instances are within these classes, as well as to synthesize practical managerial insights that a decision maker could follow in order to increase the chances that balanced groups can be found.

Suggested Citation

  • Krass, Dmitry & Ovchinnikov, Anton, 2010. "Constrained group balancing: Why does it work," European Journal of Operational Research, Elsevier, vol. 206(1), pages 144-154, October.
    • Handle: RePEc:eee:ejores:v:206:y:2010:i:1:p:144-154
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00116-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. K R Baker & S G Powell, 2002. "Methods for assigning students to groups: a study of alternative objective functions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(4), pages 397-404, April.
    2. Dmitry Krass & Anton Ovchinnikov, 2006. "The University of Toronto’s Rotman School of Management Uses Management Science to Create MBA Study Groups," Interfaces, INFORMS, vol. 36(2), pages 126-137, April.
    3. Steiner, George & Yeomans, Julian Scott, 1996. "Optimal level schedules in mixed-model, multi-level JIT assembly systems with pegging," European Journal of Operational Research, Elsevier, vol. 95(1), pages 38-52, November.
    4. Prabhakant Sinha & Andris A. Zoltners, 2001. "Sales-Force Decision Models: Insights from 25 Years of Implementation," Interfaces, INFORMS, vol. 31(3_supplem), pages 8-44, June.
    5. J Desrosiers & N Mladenović & D Villeneuve, 2005. "Design of balanced MBA student teams," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(1), pages 60-66, January.
    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. Lai, Xiangjing & Hao, Jin-Kao, 2016. "Iterated maxima search for the maximally diverse grouping problem," European Journal of Operational Research, Elsevier, vol. 254(3), pages 780-800.
    2. Lai, Xiangjing & Hao, Jin-Kao & Fu, Zhang-Hua & Yue, Dong, 2021. "Neighborhood decomposition based variable neighborhood search and tabu search for maximally diverse grouping," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1067-1086.
    3. Yang, Xiao & Cai, Zonghui & Jin, Ting & Tang, Zheng & Gao, Shangce, 2022. "A three-phase search approach with dynamic population size for solving the maximally diverse grouping problem," European Journal of Operational Research, Elsevier, vol. 302(3), pages 925-953.
    4. Schulz, Arne, 2021. "The balanced maximally diverse grouping problem with block constraints," European Journal of Operational Research, Elsevier, vol. 294(1), pages 42-53.
    5. Arne Schulz, 2022. "A new mixed-integer programming formulation for the maximally diverse grouping problem with attribute values," Annals of Operations Research, Springer, vol. 318(1), pages 501-530, November.
    6. Binyamin Krauss & Jon Lee & Daniel Newman, 2013. "Optimizing the Assignment of Students to Classes in an Elementary School," INFORMS Transactions on Education, INFORMS, vol. 14(1), pages 39-44, 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. Theresa M. Roeder & Robert M. Saltzman, 2014. "Schedule-Based Group Assignment Using Constraint Programming," INFORMS Transactions on Education, INFORMS, vol. 14(2), pages 63-72, February.
    2. Andrew Bowers & Melissa R. Bowers & Nana Bryan & Paolo Letizia & Spencer Murphy, 2023. "Forming Student Teams to Incorporate Soft Skills and Commonality of Schedule," Interfaces, INFORMS, vol. 53(2), pages 111-127, March.
    3. Dmitry Krass & Anton Ovchinnikov, 2006. "The University of Toronto’s Rotman School of Management Uses Management Science to Create MBA Study Groups," Interfaces, INFORMS, vol. 36(2), pages 126-137, April.
    4. Sergio García & Valentina Cacchiani & Lieselot Vanhaverbeke & Martin Bischoff, 2014. "The table placement problem: a research challenge at the EWI 2007," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 208-226, April.
    5. Stephen Mahar & Wayne Winston & P. Daniel Wright, 2013. "Eli Lilly and Company Uses Integer Programming to Form Volunteer Teams in Impoverished Countries," Interfaces, INFORMS, vol. 43(3), pages 268-284, May-June.
    6. Kayse Lee Maass & Vera Mann Hey Lo & Anna Weiss & Mark S. Daskin, 2015. "Maximizing Diversity in the Engineering Global Leadership Cultural Families," Interfaces, INFORMS, vol. 45(4), pages 293-304, August.
    7. Sumitro Banerjee & Alex P. Thevaranjan, 2013. "How to deal with unprofitable customers? A salesforce compensation perspective," ESMT Research Working Papers ESMT-13-05, ESMT European School of Management and Technology.
    8. Nahid Rezaeinia & Julio César Góez & Mario Guajardo, 2022. "Efficiency and fairness criteria in the assignment of students to projects," Annals of Operations Research, Springer, vol. 319(2), pages 1717-1735, December.
    9. Haofeng Jin & Zhentong Lu, 2021. "Measuring the Effectiveness of Salespeople: Evidence from a Cold-Drink Market," Staff Working Papers 21-40, Bank of Canada.
    10. Xiaojing Dong & Pradeep Chintagunta & Puneet Manchanda, 2011. "A new multivariate count data model to study multi-category physician prescription behavior," Quantitative Marketing and Economics (QME), Springer, vol. 9(3), pages 301-337, September.
    11. Du, Shaofu & Wang, Lei & Hu, Li & Zhu, Yangguang, 2019. "Platform-led green advertising: Promote the best or promote by performance," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 128(C), pages 115-131.
    12. Anton Ovchinnikov & Joseph Milner, 2008. "Spreadsheet Model Helps to Assign Medical Residents at the University of Vermont's College of Medicine," Interfaces, INFORMS, vol. 38(4), pages 311-323, August.
    13. Edward I. Brody, 2001. "Marketing Engineering at BBDO," Interfaces, INFORMS, vol. 31(3_supplem), pages 74-81, June.
    14. Z P Fan & Y Chen & J Ma & S Zeng, 2011. "Erratum: A hybrid genetic algorithmic approach to the maximally diverse grouping problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1423-1430, July.
    15. Ioanna Makarouni & John Psarras & Eleftherios Siskos, 2015. "Interactive bicriterion decision support for a large scale industrial scheduling system," Annals of Operations Research, Springer, vol. 227(1), pages 45-61, April.
    16. Binyamin Krauss & Jon Lee & Daniel Newman, 2013. "Optimizing the Assignment of Students to Classes in an Elementary School," INFORMS Transactions on Education, INFORMS, vol. 14(1), pages 39-44, September.
    17. Arne Schulz, 2023. "The balanced maximally diverse grouping problem with integer attribute values," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-27, July.
    18. Korkmazel, Tugrul & Meral, Sedef, 2001. "Bicriteria sequencing methods for the mixed-model assembly line in just-in-time production systems," European Journal of Operational Research, Elsevier, vol. 131(1), pages 188-207, May.
    19. Germann, Frank & Lilien, Gary L. & Rangaswamy, Arvind, 2013. "Performance implications of deploying marketing analytics," International Journal of Research in Marketing, Elsevier, vol. 30(2), pages 114-128.
    20. Daniel Gahler & Harald Hruschka, 2022. "Resource allocation procedures for unknown sales response functions with additive disturbances," Journal of Business Economics, Springer, vol. 92(6), pages 997-1034, August.

    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:eee:ejores:v:206:y:2010:i:1:p:144-154. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.