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

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.

Automated summary

This paper proposes robust optimization models for the distribution network design problem in a collaborative context to address uncertainty cases. Utilizing mixed-integer linear programming formulations, the study examines the economic and environmental aspects of sustainability to minimize logistical costs and CO2 emissions. A case study in France validates the models, demonstrating the impacts of uncertainty on logistical costs and CO2 emissions by comparing robust and deterministic models.