A new mathematical formulation for the static demand responsive transport problem

Demand responsive transport is a new transportation mode aiming to make the transportation system easier and more flexible. This mode allows passengers to be carried to their destinations through a set of transportation requests established by customers. These requests are to be answered by a single depot with different vehicle configurations. The idea is to group a number of passengers in the same vehicle respecting of the capacity of each vehicle in order to reduce the operational cost while maintaining a good quality of service. In this paper, we treated the static case of demand responsive transport problem. A new mathematical model for this problem is presented aiming to optimise the cost and the quality of service. This model integrates an original concept; penalty concept to enhance the quality of service. The model is validated on small and medium size instances.