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Constrained group balancing: Why does it work

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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