Delivery routing for a mixed fleet of conventional and electric vehicles with road restrictions

The enforcement of stringent regulations capping carbon emissions has prompted city logistics enterprises to substitute electric vehicles (EVs) for conventional vehicles (CVs). For city logistics enterprises with a mixed fleet of CVs and EVs, this study investigates the delivery routing problem with road restrictions (DRPRR) for accessible time windows and bearing weight. We formulate the DRPRR as a mixed integer programming model to minimise the total operations cost. The model consists of the set-up cost of CVs and EVs, the diesel cost of CVs, the electricity cost of EVs, the carbon tax cost, and the penalty cost of vehicles waiting for roads to be accessible. To effectively solve the model, an adaptive large neighbourhood search (ALNS) algorithm is developed that consists of tailored destroy and repair operators with two alternative solution acceptance criteria. Numerical experiments are conducted to validate the effectiveness of the proposed model and ALNS algorithm. In small-scale instances, the ALNS with the Metropolis criterion finds the best solutions for 41 of 48 instances while maintaining a deviation of less than 2.5% from CPLEX in the remaining 7 instances, and its running time is significantly shorter than CPLEX. In large-scale instances, the ALNS with the Metropolis criterion has stronger solving ability and better stability than benchmark algorithms (i.e. GA-LS, LNS, and ALNS with a threshold acceptance criterion). We also address a real-world case and conduct a sensitivity analysis to provide useful managerial insights. Specifically, implementing road restrictions on accessible time windows and the carbon tax policy simultaneously is more appropriate from the comprehensive perspective of market activity and carbon emissions.