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A Robust Mixed-Integer Linear Programming Model for Sustainable Collaborative Distribution

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  • Islem Snoussi

    (INSSET, University of Picardie Jules Verne, 02100 Saint-Quentin, France
    IUT de Montreuil, University of Paris 8, 93100 Montreuil, France)

  • Nadia Hamani

    (INSSET, University of Picardie Jules Verne, 02100 Saint-Quentin, France)

  • Nassim Mrabti

    (INSSET, University of Picardie Jules Verne, 02100 Saint-Quentin, France)

  • Lyes Kermad

    (IUT de Montreuil, University of Paris 8, 93100 Montreuil, France)

Abstract

In this paper, we propose robust optimisation models for the distribution network design problem (DNDP) to deal with uncertainty cases in a collaborative context. The studied network consists of collaborative suppliers who satisfy their customers’ needs by delivering their products through common platforms. Several parameters—namely, demands, unit transportation costs, the maximum number of vehicles in use, etc.—are subject to interval uncertainty. Mixed-integer linear programming formulations are presented for each of these cases, in which the economic and environmental dimensions of the sustainability are studied and applied to minimise the logistical costs and the CO 2 emissions, respectively. These formulations are solved using CPLEX. In this study, we propose a case study of a distribution network in France to validate our models. The obtained results show the impacts of considering uncertainty by comparing the robust model to the deterministic one. We also address the impacts of the uncertainty level and uncertainty budget on logistical costs and CO 2 emissions.

Suggested Citation

  • Islem Snoussi & Nadia Hamani & Nassim Mrabti & Lyes Kermad, 2021. "A Robust Mixed-Integer Linear Programming Model for Sustainable Collaborative Distribution," Mathematics, MDPI, vol. 9(18), pages 1-27, September.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2318-:d:638966
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    References listed on IDEAS

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    Cited by:

    1. Nassim Mrabti & Nadia Hamani & Laurent Delahoche, 2022. "A Comprehensive Literature Review on Sustainable Horizontal Collaboration," Sustainability, MDPI, vol. 14(18), pages 1-38, September.
    2. Alikhani, Reza & Eskandarpour, Majid & Jahani, Hamed, 2023. "Collaborative distribution network design with surging demand and facility disruptions," International Journal of Production Economics, Elsevier, vol. 262(C).
    3. Zhengying Cai & Yuanyuan Yang & Xiangling Zhang & Yan Zhou, 2022. "Design a Robust Logistics Network with an Artificial Physarum Swarm Algorithm," Sustainability, MDPI, vol. 14(22), pages 1-24, November.
    4. Mrabti, Nassim & Hamani, Nadia & Boulaksil, Youssef & Amine Gargouri, Mohamed & Delahoche, Laurent, 2022. "A multi-objective optimization model for the problems of sustainable collaborative hub location and cost sharing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).

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