Route optimization of simultaneous delivery and pick-up in automotive inbound logistics under the milk-run mode in a dual-carbon background

Purpose Under the “dual-carbon” goal, this study optimized the Two-echelon Vehicle Routing Problem with Time Windows and Simultaneous Delivery and Pickup (2E-VRPSPDTW) in automotive inbound logistics under a milk-run mode to minimize the total cost and carbon emissions while maximizing time-window satisfaction. Design/methodology/approach A novel multi-objective mixed-integer programming model was developed for a three-echelon network comprising suppliers, distribution centers and an original equipment manufacturer. The model incorporates industry-specific constraints, such as two-stage operations, differentiated volume constraints for nested empty and loaded containers and time-window satisfaction requirements. An improved non-dominated sorting genetic algorithm II (NSGA-II) with enhanced operators was designed. Findings Validation using real third-party logistics provider data shows that the algorithm outperforms benchmarks (MOEA/D, SPEA2 and Pareto-TS) in terms of solution quality, convergence and diversity, particularly for small-to-medium instances. Furthermore, sensitivity analysis confirmed that carbon tax and time-penalty costs significantly influence routing decisions and system performance. Originality/value This study clarifies the essential differences between the classical VRPSPDTW and the 2E-VRP by treating empty container flow as an active management variable. It incorporates the physical characteristics of nested empty containers and double-carbon constraints, thus providing a targeted modeling framework and an efficient algorithm for the synergistic optimization of economic, environmental and service benefits in automotive inbound logistics.