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The balanced maximally diverse grouping problem with block constraints

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  • Schulz, Arne

Abstract

The paper investigates the assignment of items to groups such that all groups are balanced, i.e. all groups contain the same number of items and all pairs of groups are as homogeneous as possible regarding the attribute values of the assigned items. Therefore, we adapt the maximally diverse grouping problem (MDGP). It is especially known in the context of students being assigned to groups. We describe the set of optimal solutions for the MDGP for realistic input data and develop a new linear objective function to determine the best balanced solution amongst all optimal solutions for the MDGP by weighting the biggest diversity between two groups with a higher value than the second biggest and so on. Furthermore, an integer program, a detailed complexity analysis, and a computational study are presented.

Suggested Citation

  • Schulz, Arne, 2021. "The balanced maximally diverse grouping problem with block constraints," European Journal of Operational Research, Elsevier, vol. 294(1), pages 42-53.
    • Handle: RePEc:eee:ejores:v:294:y:2021:i:1:p:42-53
    DOI: 10.1016/j.ejor.2021.01.029
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    Cited by:

    1. Christian Pfeiffer & Arne Schulz, 2022. "An ALNS algorithm for the static dial-a-ride problem with ride and waiting time minimization," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 87-119, March.
    2. 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.
    3. Arne Schulz, 2024. "Efficient neighborhood evaluation for the maximally diverse grouping problem," Annals of Operations Research, Springer, vol. 341(2), pages 1247-1265, October.
    4. 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.

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