Today, many transportation systems use hub-and-spoke structures to transfer flow from origin to destination. In such systems, making the right and timely decisions about facilities during the planning horizon is crucial for Decision-Maker (DM); because the parameters influencing decision-making change over the planning horizon, and the initial design of the transportation network may not be desirable for the future. In this paper, we present a novel mathematical programming model for designing a multi-period hub network in a continuous-time planning horizon, considering linear time-dependent demand. The proposed model is a non-linear programming model in which sustainability aspects are addressed through the following objectives: economic (minimizing network costs), environmental (minimizing emissions), and social (maximizing fixed and variable job opportunities). After linearizing the model, using the aggregation function of the Torabi–Hassini (TH) method, the model becomes a parametric single-objective model, and some valid inequalities are introduced. To solve the single-objective model, an accelerated Benders decomposition algorithm and a rolling horizon heuristic algorithm are proposed. The proposed heuristic method can solve problems with twenty-five nodes and six time periods on the CAB dataset. Pareto solutions provide optimal decisions about facilities location, adjusting the operational capacity of facilities (through modules), and routing flows for DM. Also, the best time to implement decisions and the satisfaction degree of sustainability objectives are determined for each solution. We also perform sensitivity analysis on important parameters. The results show that the cost of designing a network with economic and social objectives is more than the cost of designing a network with economic and environmental objectives. Also, by increasing the module capacity after a threshold value, the network costs remain constant.
