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Physarum solver: a bio-inspired method for sustainable supply chain network design problem

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Abstract

A supplier of products and services aims to minimize the capacity investment cost and the operational cost incurred by unwanted byproducts, e.g. carbon dioxide emission. In this paper, we consider a sustainable supply chain network design problem, where the capacity and the product flow along each link are design variables. We formulate it as a multi-criteria optimization problem. A bio-inspired algorithm is developed to tackle this problem. We illustrate how to design a sustainable supply chain network in three steps. First, we develop a generalized model inspired by the foraging behaviour of slime mould Physarum polycephalum to handle the network optimization with multiple sinks. Second, we propose a strategy to update the link cost iteratively, thus making the Physarum model to converge to a user equilibrium. Third, we perform an equivalent operation to transform a system optimum problem into a corresponding user equilibrium problem so that it is solvable in the Physarum model. The efficiency of the proposed algorithm is illustrated with numerical examples.

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Adopted from Nagurney and Nagurney (2010)

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Acknowledgements

The authors greatly appreciate the reviews’ suggestions and the editor’s encouragement. The work is partially supported by National Natural Science Foundation of China (Grant Nos. 61174022, 61573290, 61503237).

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Authors and Affiliations

  1. School of Computer and Information Science, Southwest University, Chongqing, 400715, China

    Xiaoge Zhang, Sankaran Mahadevan & Yong Deng

  2. School of Engineering, Vanderbilt University, Nashville, TN, 37235, USA

    Xiaoge Zhang & Yong Deng

  3. Unconventional Computing Center, University of the West of England, Bristol, BS16 1QY, UK

    Andrew Adamatzky

  4. Department of Industrial and Systems Engineering, Hong Kong Polytechnic University, Hung Hom, Hong Kong

    Felix T. S. Chan

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  1. Xiaoge Zhang
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  2. Andrew Adamatzky
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  4. Sankaran Mahadevan
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  5. Yong Deng
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Correspondence to Yong Deng.

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Zhang, X., Adamatzky, A., Chan, F.T.S. et al. Physarum solver: a bio-inspired method for sustainable supply chain network design problem. Ann Oper Res 254, 533–552 (2017). https://doi.org/10.1007/s10479-017-2410-x

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  • DOI: https://doi.org/10.1007/s10479-017-2410-x

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