Compensation and profit allocation for collaborative multicenter vehicle routing problems with time windows

With the growing interest in win–win cooperation within the logistics industry recently, collaborative multicenter logistics networks have witnessed the establishment of numerous alliances aimed at achieving cost savings. However, alliance members may choose to withdraw from an alliance due to changes in market positioning strategies and short-term profit considerations. Such withdraws often lead to the disintegration of the alliance and result in financial losses for the remaining non-defaulting members. This study focuses on addressing the issues of compensation and profit allocation in a specific scenario known as the collaborative multicenter vehicle routing problem with time windows and defaulting members withdrawal (CMVRPTWDMW). The objective is to ensure alliance stability and fair profit distribution among its members. To achieve this, a tri-objective mathematical model is proposed to optimize the re-formed alliances by considering the total operating cost, number of vehicles, and service waiting time. Additionally, an improved minimum cost remaining saving method is introduced to accurately quantify the deserved profits of non-defaulting members. Compensation quantification and default cost allocation models are then developed based on this analysis. To solve the CMVRPTWDMW and obtain Pareto optimal solutions, a hybrid heuristic algorithm is designed. This algorithm combines a 3D k-means clustering algorithm for customer reassignment after the withdrawal of defaulting members, effectively reducing the complexity of the problem. Furthermore, the algorithm employs a Clarke-Wright saving method-based non-dominated sorting genetic algorithm-III (CW-NSGA-III) to search for optimal solutions. To enhance the algorithm’s search ability, an elite alteration strategy and a penalty-based boundary intersection approach are incorporated into CW-NSGA-III. Finally, a real-world case study conducted in Chongqing City, China, is presented to demonstrate the feasibility of the proposed models and solution algorithms. The study contributes valuable insights into the sustainable operation of urban logistics networks that may experience unpredictable defaults, providing guidance for the stability of logistics alliances in the transportation sector.