Stochastic Dynamic Model of City Bus Routes and Their Optimum Management

In this paper, we develop a stochastic dynamic model for the city bus route subject to practical constraints. We define an objective functional based on the expressions for fuel cost, operating cost, customers waiting time, and revenue of the bus company. Following this, an optimization problem is formulated and solved using calculus of variations. It is expected to improve the bus company's revenue, reduce customers waiting time and promote their satisfaction if the solution presented here is implemented. The system is simulated with a series of numerical experiments and the corresponding optimization problems are solved giving the optimal number of buses allocated to a bus route. Since the dynamic model can be generally applied to any bus route, it is strongly believed that the procedure developed in this paper has a great potential of benefits for both the city bus company and the customers served.