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 CO₂ 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 CO₂ emissions.

中文翻译：

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用于可持续协作分布的稳健混合整数线性规划模型

在本文中，我们为配电网络设计问题 (DNDP) 提出了稳健的优化模型，以处理协作环境中的不确定性情况。所研究的网络由协作供应商组成，这些供应商通过通用平台交付产品来满足客户的需求。几个参数——即需求、单位运输成本、最大使用车辆数等——受区间不确定性的影响。针对这些案例中的每一个都提出了混合整数线性规划公式，其中研究并应用了可持续性的经济和环境维度，以最大限度地减少物流成本和 CO ₂排放量，分别。这些公式是使用 CPLEX 求解的。在这项研究中，我们提出了一个法国分销网络的案例研究来验证我们的模型。通过比较稳健模型和确定性模型，获得的结果显示了考虑不确定性的影响。我们还解决了不确定性水平和不确定性预算对物流成本和 CO ₂排放的影响。