Continuous-Time Multi-Period Planar Hub Location Considering Stochastic Time-Dependent Demand : A Hybrid Approach

In transportation systems with mobile and modular facilities, decisions related to facility location and facility capacity management during the planning horizon are critical; because the parameters effective in these decisions change over time, and it is necessary for the decision-maker to adjust the location and capacity of the facilities at specific times during the planning horizon to coordinate with the changes in the parameters. This paper studies a multi-period planar hub location problem considering stochastic time-dependent demand and modular capacity of hubs in a continuous-time planning horizon. The problem is formulated as a mixed-integer nonlinear programming model, and to improve the formulation, some valid inequalities are presented. To solve the model, a dynamic programming-based hybrid method is presented, in which some algorithms (drop and interchange, simple allocation, allocation improvement, hyperbolic approximation procedure, and cost calculation) are used to calculate the cost of decisions in different states. The results of solving the problem on the AP dataset are reported for instances with up to a hundred nodes and eight hubs. Also, the results of sensitivity analysis of the important parameters of the problem are presented. The results show that in the uncertain case, the sum of the modules installed on each hub in the entire planning horizon is more than in the case where the uncertain parameters take their mean value