Abstract: The significant increase of diversified logistics demands and the shortage of logistics resources call for the multi-center pickup and delivery network optimization in terms of resource coordination. In order to improve the utilization of resources in a multi-center distribution network, multiple logistics enterprises realize resource re-coordination and optimization via alliances. However, in practice, there can be a critical default situation that alliance members withdraw from collaboration due to strategy changes. Designing a reasonably compensation mechanism can guarantee the stability of an alliance and maintain long-term partnerships. To overcome the deficiencies of developing network alliances and designing the mechanisms for default penalties and loss compensations in the multi-center pickup and delivery network optimization study, an alliance optimization strategy for the multi-center pickup and delivery network is proposed considering both default penalties and loss compensations in collaboration. First, the minimum costs remaining saving method based on the importance of non-default members is proposed to study the deserved profits of the non-default members, and then two models are proposed to quantify the deserved loss compensations for non-default members and the default penalties of their counterparts, respectively. Second, considering the contract default resulting in changing customer service relationships, a multi-objective programming model is formulated to minimize the total operating cost, number of vehicles, and service waiting time within the network. Third, a hybrid heuristic algorithm integrating the K-means multi-dimensional clustering algorithm and the Clarke-Wright saving method-based non-dominated sorting genetic algorithm-Ⅲ (CW-NSGA-Ⅲ) is then proposed to solve the model. The Clarke-Wright saving algorithm is applied to improve the quality of the initial population, and the elite retention strategy is used to enhance search performance. The search path deviation penalty-based boundary intersection approach is introduced to improve the selection mechanism of non-dominated solutions and enhance the diversity and convergence of non-dominated solution sets. In addition, the proposed hybrid algorithm is compared and validated with the multi-objective genetic algorithm (MOGA), the multi-objective harmony search algorithm (MOHSA), and the multi-objective particle swarm optimization (MOPSO), respectively. Finally, the proposed model and algorithm are illustrated and demonstrated via a case study, and the optimization results of the multi-center pickup and delivery network under different default situations and withdrawal modes of customers are compared and analyzed. Results show that the proposed approach can quantify the default cost of default members, guarantee the deserved profits of non-default ones, and optimize the multi-center pickup and delivery network when contract default occurs, thus enriching the collaboration mechanism for alliance members. Furthermore, this study provides a reliable theoretical basis and decision support for the sustainable development of urban multi-center logistics networks.

Key words: multi-center pickup and delivery network; network alliance; default penalty; loss compensation; CW-NSGA-Ⅲ algorithm