Multi-Objective Model for Dial-a-Ride Problems with Vehicle Speed Considerations

Mobility on demand (MOD) provides improved mobility options to all travelers with the use of on-demand information and real-time data. Several alternatives, such as Demand Responsive Transit Systems (DRTS) services, have been introduced around the world. Early DRTS provide on-demand service for areas of low-density population. Nowadays, DRTS are mostly used to provide door-to-door services, and this specific type of DRTS is called Dial-a-Ride Problems (DARP). In this study, a multi-objective model with three objectives, including travel cost, service quality, and eco-efficiency, is formulated. Travel cost is estimated through vehicle travel time, service quality is measured as customer waiting time, and eco-efficiency is measured through consumed fuel. A speed-level variable is introduced in the DARP model to describe travel time, waiting, and consumed fuel simultaneously. For each objective, a single objective model is constructed and implemented. Then, the weighting method with normalization (WMN) is applied for the multi-objective model to solve three objectives. The proposed model is solved through the Gurobi optimizer. Numerical experiments are conducted based on real geometric data in Kaohsiung City. The results show that the proposed model not only provides compromise solutions, but also improves the total performance in meeting three objectives. Pareto front is analyzed with many different combinations of weights to provide more information about the trade-offs between the three objectives. The results can be applied in practice to design vehicle routes for operators and to design DARP evaluation criteria for official agencies.