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Measures of balance in combinatorial optimization

Author

Listed:
  • Philippe Olivier

    (Polytechnique Montréal
    Canada Excellence Research Chair)

  • Andrea Lodi

    (Polytechnique Montréal
    Canada Excellence Research Chair)

  • Gilles Pesant

    (Polytechnique Montréal)

Abstract

The concept of balance plays an important role in many combinatorial optimization problems. Yet there exist various ways of expressing balance, and it is not always obvious how best to achieve it. In this methodology-focused paper, we study three cases where its integration is deficient and analyze the causes of these inadequacies. We examine the characteristics and performance of the measures of balance used in these cases, and provide general guidelines regarding the choice of a measure.

Suggested Citation

  • Philippe Olivier & Andrea Lodi & Gilles Pesant, 2022. "Measures of balance in combinatorial optimization," 4OR, Springer, vol. 20(3), pages 391-415, September.
    • Handle: RePEc:spr:aqjoor:v:20:y:2022:i:3:d:10.1007_s10288-021-00486-x
    DOI: 10.1007/s10288-021-00486-x
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    References listed on IDEAS

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    1. Schuijbroek, J. & Hampshire, R.C. & van Hoeve, W.-J., 2017. "Inventory rebalancing and vehicle routing in bike sharing systems," European Journal of Operational Research, Elsevier, vol. 257(3), pages 992-1004.
    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    3. Sara Ceschia & Luca Di Gaspero & Andrea Schaerf, 2014. "The generalized balanced academic curriculum problem with heterogeneous classes," Annals of Operations Research, Springer, vol. 218(1), pages 147-163, July.
    4. C Mullinax & M Lawley, 2002. "Assigning patients to nurses in neonatal intensive care," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(1), pages 25-35, January.
    5. Gilles Pesant, 2015. "Achieving Domain Consistency and Counting Solutions for Dispersion Constraints," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 690-703, November.
    6. Marsh, Michael T. & Schilling, David A., 1994. "Equity measurement in facility location analysis: A review and framework," European Journal of Operational Research, Elsevier, vol. 74(1), pages 1-17, April.
    7. Ogryczak, Wlodzimierz, 2000. "Inequality measures and equitable approaches to location problems," European Journal of Operational Research, Elsevier, vol. 122(2), pages 374-391, April.
    8. Marian Rainer-Harbach & Petrina Papazek & Günther Raidl & Bin Hu & Christian Kloimüllner, 2015. "PILOT, GRASP, and VNS approaches for the static balancing of bicycle sharing systems," Journal of Global Optimization, Springer, vol. 63(3), pages 597-629, November.
    9. Brahim Hnich & Zeynep Kiziltan & Ian Miguel & Toby Walsh, 2004. "Hybrid Modelling for Robust Solving," Annals of Operations Research, Springer, vol. 130(1), pages 19-39, August.
    10. Claudia D’Ambrosio & Andrea Lodi, 2013. "Mixed integer nonlinear programming tools: an updated practical overview," Annals of Operations Research, Springer, vol. 204(1), pages 301-320, April.
    Full references (including those not matched with items on IDEAS)

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