Collaborative multidepot split delivery network design with three-dimensional loading constraints

The growing demand for bulky goods has spurred logistics firms to explore how to effectively manage and optimize multidepot delivery networks that consider three-dimensional loading constraints. The ability to divide customer demands and adaptively adjust vehicle compartments has significantly enhanced delivery efficiency and vehicle resource utilization. This study develops a collaborative multidepot vehicle routing problem that accommodates split deliveries and three-dimensional loading constraints. It begins by formulating a multi-objective mathematical model that aims to minimize total operating costs (TOC) and the number of vehicles used (NV) while maximizing the average loading rate (ALR). A novel hybrid algorithm combining an improved k-nearest neighbor clustering algorithm with an adaptive non-dominated sorting genetic algorithm-III (ANSGA-III) is developed to find Pareto optimal solutions. The improved knearest neighbor clustering algorithm is applied for the reallocation of customers. The ANSGA-III incorporates elite alteration and adaptive information feedback mechanisms to enhance the solution quality and algorithm convergence. Strategies for split loads and vehicle compartment partition are integrated into the ANSGA-III, facilitating the improvement of vehicle resource configuration efficiency. The superiority of the proposed algorithm is verified by comparison with those of the CPLEX solver for small-scale problems and against multi-objective particle swarm optimization, multi-objective evolutionary algorithms, and multi-objective ant colony optimization for medium-to-large problems. Additionally, the proposed model and algorithm are applied to a real-world case study in Chongqing city, China, and the result comparison from the initial network to optimized network shows that the TOC and NV reduced by 43.57% and 32.14%, respectively, while the ALR is improved by 33.51%. Furthermore, this study discusses the optimized results under varying the vehicle compartment partition strategies, contributing to the superiority of proposed approach in improving vehicle resource utilization efficiency. This represents significant cost savings of $2,934 and a reduction of six vehicles, along with a notable 23.35%% improvement in ALR compared to the scenario without compartment division. We also discuss various scenarios involving the split load strategies and different loading capacity schemes, and the computational results demonstrate that the proposed approach improves vehicle loading rates and reduces logistics operating costs. Specifically, the result comparison between