A p-center mobile hub location in a dynamic environment with capacity constraints and multiple allocation

In this paper, the problem of p-center mobile hub location with capacity constraint is studied. According to the rapid developments, paying attention to strategic decisions is considered a significant factor in network design. Thus, the dynamic model is considered to adapt to environmental changes; also, the movability and mobility are simultaneously provided for the hubs in the subsequent periods. Multiple allocations are deemed to connect demand nodes to the hubs to tackle capacity constraints in hubs. A bi-objective model is also employed, which is as follows: the first aim is to reduce travel times, and the second aim is to minimize network costs; As a result, the quality and level of response to demands can be increased. In addition, we attempted to use both classical and intelligent methods for the proposed multi-objective model. The goal programming method and AP dataset are employed for sensitivity analysis and validation, and the Goal attainment method is used to solve the model in small dimensions. Besides, the NSGA-II and MOPSO are developed and used as intelligent methods to approximate the Pareto front of the model in small and large dimensions. Also, a local search algorithm is considered within the intelligent algorithms to calculate the optimal values of the model decision variables. The parameters in intelligent algorithms are tuned using the Taguchi method. Finally, classical and intelligent solutions' results are examined and compared based on five different evaluation criteria. The results of comparisons prove that the Goal attainment method outperforms NSGA-II and MOPSO, and the NSGA-II is better than the MOPSO.