عنوان مقاله [English]
Today, many transportation systems use hub and spoke structures to transfer flow (good, message, passenger, etc.) from origin to destination. In such systems, the manager must plan for the location of the hubs and the allocation of other demand points to the hubs and other decisions during the planning horizon. Also, if the planning horizon is continuous time, the manager must also determine the timing of implementing the decisions. To determine the optimal decisions during the planning horizon and the best time for implementing decisions (i.e., breakpoints) according to sustainability aspects. In this research, a mathematical programming model is presented for a sustainable multi-period hub location problem in which the transportation demand between different origin-destination pairs is time-dependent and the planning horizon is continuous-time. The problem is formulated as a nonlinear multi-objective mixed integer programming model. Sustainability aspects are
considered as objectives of the model. These objectives are minimizing transportation system costs, minimizing emissions in the transportation
network, and maximizing fixed and variable job opportunities created by hubs during the planning horizon. Also, some valid inequalities are presented for strengthening the formulation of the problem. To solve the problem, we first use the Augmented Epsilon Constraint method version 2 (AUGMECON2) and then, use a dynamic programming approach to determine the optimal values of the breakpoints of the planning horizon. Using the proposed dynamic programming method, in each stage, some of decision variables are fixed and the number of
variables in the original problem is reduced and instead of a nonlinear mixed integer programming problem, we solve a mixed integer linear programming problem that is easier to solve. The results of the solution methods are presented for a sample problem on the Turkish network dataset. Also, the CAB dataset is used to validate the dynamic programming method. The results show that the dynamic programming approach can solve problems with up to 25 nodes and 6 time periods.