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Designing closed-loop supply chains with nonlinear dimensioning factors using ant colony optimization

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Abstract

Closed-loop supply chain (CLSC) design implies the modelling of the forward and the reverse flows of products in an integrated way. This paper introduces nonlinear dimensioning factors in the design of CLSC and uses ant colony optimization to optimize the design of the supply chain. The proposed algorithm is called SCAnt-NLDesign. The modelled nonlinear dimensioning factors are: cost variations in transportation distances between facilities (tapering principle), scale economies related to transported quantities, and scale economies regarding the facilities’ capacity. Results show that the proposed SCAnt-NLDesign algorithm reduced the total cost in 44 %, when compared to a linear formulation of a CLSC. Note also that a mixed integer linear programming implementation of the nonlinear CLSC was not able to get closed to the optimal solution, given worse results than the linear CLSC.

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Notes

  1. A directed graph, also known as a network, is a finite set of nodes and a set of edges that are defined as ordered pairs of nodes. This order implies a one-way connection between nodes. If a scalar weight is associated with every edge the directed graph is called edge-weighted (Christou 2012).

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Acknowledgments

This work is supported by the FCT project PTDC/SEN-ENR/100063/2008, co-sponsored by FEDER, Programa Operacional Ciência e Inovação 2010, FCT, Portugal, and by the FCT Grant SFRH/BPD/65215/2009, Fundação para a Ciência e a Tecnologia, Ministério do Ensino Superior, da Ciência e da Tecnologia, Portugal, and by the European Science Fundation, under the COST action IC0702 “Combining Soft Computing Techniques and Statistical Methods to Improve Data Analysis Solutions”.

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Authors and Affiliations

  1. LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001, Lisboa, Portugal

    P. F. Vieira, S. M. Vieira & J. M. C. Sousa

  2. Centro de Matemática e Aplicações, Faculdade de Ciências e Tecnologia, New University of Lisbon, 2829-516 , Caparica, Portugal

    M. I. Gomes

  3. Center for Management Studies (CEG-IST), Instituto Superior Técnico, Universidade de Lisboa, 2780-990 , Porto Salvo, Portugal

    A. P. Barbosa-Póvoa

Authors
  1. P. F. Vieira
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  2. S. M. Vieira
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  3. M. I. Gomes
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  4. A. P. Barbosa-Póvoa
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  5. J. M. C. Sousa
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Correspondence to J. M. C. Sousa.

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Communicated by V. Loia.

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Vieira, P.F., Vieira, S.M., Gomes, M.I. et al. Designing closed-loop supply chains with nonlinear dimensioning factors using ant colony optimization. Soft Comput 19, 2245–2264 (2015). https://doi.org/10.1007/s00500-014-1405-7

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