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The objective of vehicle routing problem is usually to minimize the total traveling distance or cost. But in practice, there are a lot of problems needed to minimize the fastest completion time. The milk-run vehicle routing problem (MRVRP) is widely used in milk-run distribution. The mutation ACO is given to solve MRVRP with fastest completion time in this paper. The milk-run VRP with fastest completion time is introduced first, and then the customer division method based on dynamic optimization and split algorithm is given to transform this problem into finding the optimal customer order. At last the mutation ACO is given and the numerical examples verify the effectiveness of the algorithm.

This study explores a road–rail intermodal routing problem. To improve the carbon efficiency of transportation, reducing CO2 emissions is considered by the routing. Soft time windows are incorporated into the routing to optimize the timeliness of the first-mile pickup and last-mile delivery services in intermodal transportation. The routing is further modeled in a time-dependent and fuzzy environment where the average truck speeds of the road depend on the truck departure times and are simultaneously considered fuzzy along with rail capacities. The fuzzy truck speed leads to the fuzziness of three aspects, including speed-dependent CO2 emissions of the road, a timetable-constrained transfer process from road to rail, and delivery time window violation. This study formulates the routing problem under the above considerations and carbon tax regulation as a combination of transportation path planning problem and truck departure time and speed matching problem. A fuzzy nonlinear optimization model is then established for the proposed routing problem. Furthermore, chance-constrained programming with general fuzzy measure is used to conduct the defuzzification of the model to make the problem solvable, and linearization techniques are adopted to linearize the model to enhance the efficiency of problem-solving. Finally, this study presents an empirical case to demonstrate the effectiveness of the designed approach. This case study evaluates the performance of carbon tax regulation by comparing it with multi-objective optimization. It also focuses on sensitivity analysis to discuss the influence of the optimistic–pessimistic parameter and confidence level on the optimization results. Several managerial insights are revealed based on the case study.