Traveling itinerary problem in a scheduled multimodal transportation network for a fixed sequence of cities

Developing an efficient and economical journey plan in multimodal transportation networks is of significant and fast-growing importance, but it is still an annoying experience for a traveler. This paper aims to find the journey plan at a combined cross-border and inter-regional level when visiting a sequence of cities while utilizing several transport modes to reduce travel costs and planning time. We study a traveling itinerary problem in a scheduled multimodal transportation network with constraints on both arcs and nodes as a new extension of the shortest path problem. We formulate a 0-1 integer linear programming model for the traveling itinerary problem and develop an exact algorithm that finds a combined cross-border and inter-regional low costs journey plan. We present case studies based on real-world transport data to illustrate the usefulness and computational efficiency of the proposed approaches. We compare the results with the previously proposed approach to demonstrate the benefits of multimodal journeys. Finally, we compare the results with the solution obtained by the general-purpose 0-1 integer linear programming solver to evaluate the computational time.