This paper presents a bi-objective, nonlinear mathematical model for designing a multi-period hub network, considering a polynomial function for time-dependent transportation demand. The proposed demand function can be used for various applications of the hub network design problem. Hubs’ capacity in the proposed model is considered to be modular. Each module corresponds to a number of servers at hubs. Objectives of the problem include minimizing network costs and maximizing responsiveness by minimizing the sum of the maximum travel times in all time periods. The proposed model provides the best timing for implementing decisions during the planning horizon. To solve the model, NSGA-II, NRGA, PESA-II, and SPEA-II meta-heuristics are used. To compare the performance of the solution algorithms, some multi-objective metrics and statistical tests on the CAB, AP, and TR datasets are applied. We also perform sensitivity analysis on some critical parameters. The sensitivity analysis results show that the network design with economic and responsiveness considerations simultaneously has a higher cost than the network design with only economic considerations.
