A bi-level programming model and solution algorithms for taxi fare in taxi market of China

The hearing system provides a game platform for dealing with the optimization problem of taxi fare due to the taxi market regulations and the variation of operating cost in taxi market of China. In this paper, a bi-level programming model is proposed for optimization of taxi fare in monopoly market, as simultaneously considers the equilibrium between the social welfare and profit of taxi firms. The upper- level problem is a set of formulations ensuring maximization of social welfare under constrain on taxi fare restriction of government in taxi industry. The lower-level model aims to maximize the profit of taxi firms from fare revenue and maintains the positive value of firm profit and supply-demand equilibrium of taxi market. The Lagrangian approach is used to transform the lower model into upper model with K-K-T conditions, and the bi-level programming model becomes a single-level programming model. The Genetic Algorithm and Simulated Annealing algorithm are respectively designed to solve the model. A numerical calculation is presented to illustrate the accuracy and efficiency of proposed model and algorithms in a real urban road network of Harbin.