Proposing a new mathematical formulation for modeling costs in a p-hub center problem

Generally, P-hub center problem aims to establish a hub network wherein the maximum travel times between any given pair of nodes is minimized. The distinctive feature of this paper is proposing a new mathematical formulation for modeling costs in a p-hub center problem. Here, instead of seeing costs as a linear function of distance, we, for the first time, formulated costs that consist of different parts: fixed cost, Health, Safety and Environment cost, energy cost and personnel cost. Such an integrated model results in a hard-to-solve nonlinear formulation. For a small scale standard data set the model is solved by Lingo 8.0 software but the area for solving the formulation for large scale instances is yet to be hunted.