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An optimization approach for winner determination problem considering transportation cost discounts

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Abstract

This study proposes a mixed-integer nonconvex programming (MINP) model for the winner determination problem (WDP) considering two discount functions in a combinatorial auction to save shipper’s transportation cost. For the WDP, the shipper allows carriers to submit bids for a bundle of lanes. Then the winning carries are selected by solving the WDP. Specifically, this study considers the shipment distance-based and volume-based discounts for transportation cost, simultaneously. The state-of-the-art linearization technique is available to convert the MINP model into a mixed-integer linear program (MILP) to obtain a global optimum, but the solution time becomes inefficient when the problem size becomes large. To find efficient and effective linearization techniques for large-scale WDP, this study (1) proposes a novel WDP model with discount policies, (2) utilizes superior encoding formulation to avoid the unbalanced branch-and-bound trees in solving MILP, and (3) reduces big-M constraints to speed up the solving time. The proposed method leads to significant savings in computational efforts. Numerical experiments with real-world-sized truckload service procurement problems are solved by the proposed method and further confirmed the drastic reduction in computational time for solving the large-size WDP.

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Acknowledgements

The authors would like to sincerely thank the area editor, associate editor, and two reviewers for their thoughtful and valuable comments which have significantly improved the quality of this paper. Y.-H. Huang’s research works have been supported by the Ministry of Science and Technology of Taiwan under grant MOST109-2410-H-030-037-MY3.

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Authors and Affiliations

  1. School of Economics and Management, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Fang Yang

  2. Department of Information Management, Fu Jen Catholic University, New Taipei City, 242062, Taiwan

    Yao-Huei Huang

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  1. Fang Yang
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Correspondence to Yao-Huei Huang.

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Yang, F., Huang, YH. An optimization approach for winner determination problem considering transportation cost discounts. J Glob Optim 80, 711–728 (2021). https://doi.org/10.1007/s10898-021-01035-w

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