Development of a robust multi-objective model for green capacitated location-routing under crisis conditions

Location-Routing Problem (LRP) is a strategic supply chain design problem aimed at meeting customer demands. LRPs involve selecting one or more depot sites from a set of potential locations and determining the best routes to connect them to demand points. With the rising awareness about the environmental impacts of transportation over the past years, the use of green logistics to mitigate these impacts has become increasingly important. To compensate for a gap in the literature, this paper presents a robust bi-objective mixed-integer linear programming (MILP) model for the green capacitated location-routing problem (G-CLRP) with demand uncertainty and the possibility of failure in depots and routes. The final result of this Robust Multi-Objective Model is to set up the depots and select the routes that offer the highest reliability (Maximizing network service) while imposing the lowest cost and environmental pollution. A Nondominated Sorting Genetic Algorithm (NSGA-II) is used to solve the large-sized instances of the modeled problem. The paper also provides a numerical analysis and a sensitivity analysis of the solutions of the model.