Joint Optimization of Workload Balance and Vehicle Routing Considering Three-Dimensional Loading Constraints

To improve the efficiency of logistics distribution and balance the workload of drivers, this study introduces the standard deviation of workload time as an equilibrium measure and constructs a dual-objective mixed-integer programming model based on three-dimensional loading constraints to achieve the minimum total distance and workload balance. To solve the above model, a multi-stage hybrid algorithm is designed in this paper. Firstly, the clustering algorithm is used to effectively divide the distribution area, and then the non-dominated sorting genetic algorithm is used to solve the vehicle routing problem considering workload balance. At the same time, the constructive heuristic three-dimensional loading algorithm based on block loading is invoked to ensure the feasibility of cargo loading. Based on the historical data of a material flow distribution company, the feasibility of the constructed model and algorithm is verified. The research shows that the standard deviation of workload time can be reduced by 35.86%, and the average loading rate can be increased by 9.19% under the premise of increasing the distribution distance by only 1.6%. In addition, the proposed algorithm is compared with three other multi-objective optimization algorithms by constructing examples of different scales and using a series of standard example sets to verify its effectiveness and superiority.