Modeling and solving the multi-period disruptions scheduling problem on urban networks

In the last decades, the urban mobility has become a critical issue with several social, economic and ecological challenges. This is a consequence of the fast and unplanned cities growth and of the high population density in urban areas. In this context, we focus on the Disruption Scheduling problem on Urban Networks (DSUN) which consists in scheduling a set of planned disruptions in an urban road network while ensuring a path between all points of this network (strong connectivity in graph theory). Disruptions can break the urban network connection, requiring then to modify the routes direction (arcs reversals). Such situations may disturb the users’ habits. The goal of DSUN is (1) to minimize the number of arcs reversals and (2) the sum of the starting times to all disruptions simultaneously. DSUN is formalized in this study by means of a mathematical formulation. Moreover, since it is a bi-objective problem, we propose an exact algorithm based on the $$\epsilon $$ϵ-constraint method. Computational experiments are performed on theoretical instances, as well as on realistic instances built from the road network map of Troyes city in France. The numerical results show that the exact algorithm can prove optimality for instances with up to 100 vertices and 20 disruptions.