Branch and price algorithm for route optimization on customized bus service

As an innovative public transport, the customized bus has rapidly grown. To improve the efficiency of customized bus and satisfy customers' personal requirement, a mixed-integer programming model is proposed to optimize the stop assignment for customers and route scheduling for buses with walking distance constraints and travel time constraints. As an variants of vehicle routing problem, the formulated model on large-scale instances is intractable to solve for commercial solvers. Therefore, an exact algorithm based on branch and price is developed to solve the model, in which a labeling algorithm is designed for the pricing problems. Numerical experiments and a real-world case in Dalian are conducted to validate the effectiveness of the proposed model. The computational results show that the tailored algorithm can yield an optimal solution within a significantly shorter time than that of CPLEX. Some managerial implications are also obtained based on sensitivity analysis, which may be potentially useful for bus companies.