Integrated Railway Rapid Transit Network Design and Line Planning problem with maximum profit

We solve the Integrated Network Design and Line Planning Problem in Railway Rapid Transit systems with the objective of maximizing the net profit over a planning horizon, in the presence of a competing transportation mode. Since the profitability of the designed network is closely related with passengers' demand and line operation decisions, for a given demand, a transit assignment is required to compute the profit, calculating simultaneously the frequencies of lines and selecting the most convenient train units. The proposed iterative solving procedure is governed by an adaptive large neighborhood search metaheuristic which, at each iteration, calls a branch-and-cut algorithm implemented in Gurobi in order to solve the assignment and network operation problems. We provide an illustration on a real-size scenario.