Vehicle dispatching in modular transit networks: A mixed-integer nonlinear programming model

Modular vehicle (MV) technology offers the possibility of flexibly adjusting the vehicle capacity by docking/undocking modular pods into vehicles of different sizes en route to satisfy passenger demand. Based on the MV technology, a modular transit network system (MTNS) concept is proposed to overcome the mismatch between fixed vehicle capacity and spatially varying travel demand in traditional public transportation systems. To achieve the optimal MTNS design, a mixed-integer nonlinear programming model is developed to balance the tradeoff between the vehicle operation cost and the passenger trip time cost. The nonlinear model is reformulated into a computationally tractable linear model. The linear model solves the lower and upper bounds of the original nonlinear model to produce a near-optimal solution to the MTNS design. This reformulated linear model can be solved with off-the-shelf commercial solvers (e.g., Gurobi). Two numerical examples are used to demonstrate the applicability of the proposed model and its effectiveness in reducing system costs.