Robust modeling of the multi-depot vehicle routing problem under uncertain demands

In this paper, we focus on the multi-depot vehicle routing problem with time window constraints (MDVRPTW) under uncertain demands. It constitutes a practical and challenging problem in logistics and supply chain management. When customers' demands change, using the deterministic VRP model may turn the originally feasible routing solution into an infeasible one, which eventually will lead to profit loss. To address this issue, we propose a robust model to minimize the total cost while considering the uncertainty of customers' demands. We then convert the model into a linear robust formulation and solve it using Gurobi. The experimental results verify that the robust optimization model is more reliable and resilient than the deterministic one, and can effectively suppress the perturbations caused by the demands uncertainty.