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Complementary column generation and bounding approaches for set partitioning formulations

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Abstract

We present a complementary column generation feature that produces tight upper bounds, thereby enhancing heuristic and exact column generation approaches for (minimization) set partitioning formulations that possess dense column structures. We also introduce a duality-based lower bound that prompts a useful termination criterion, which can be utilized to mitigate the tailing-off effect induced by column generation approaches. Computations are presented for the one-dimensional bin packing problem and a joint vehicle assembly-routing problem.

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Authors and Affiliations

  1. Department of Finance and Operations Management, Isenberg School of Management, University of Massachusetts, 121 Presidents Dr., Amherst, MA, 01003, USA

    Ahmed Ghoniem

  2. Grado Department of Industrial and Systems Engineering (0118), Virginia Polytechnic Institute and State University, 250 Durham Hall, Blacksburg, VA, 24061, USA

    Hanif D. Sherali

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  1. Ahmed Ghoniem
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  2. Hanif D. Sherali
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Correspondence to Ahmed Ghoniem.

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Ghoniem, A., Sherali, H.D. Complementary column generation and bounding approaches for set partitioning formulations. Optim Lett 3, 123–136 (2009). https://doi.org/10.1007/s11590-008-0097-2

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  • DOI: https://doi.org/10.1007/s11590-008-0097-2

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