Multi-vehicle synchronized arc routing problem to restore post-disaster network connectivity

After a natural disaster roads can be damaged or blocked by debris, while bridges and viaducts may collapse. This commonly observed hazard causes some road sections to be closed and may even disconnect the road network. In the immediate disaster response phase work teams are dispatched to open a subset of roads to reconnect the network. Closed roads are traversable only after they are unblocked/cleared by one of the teams. The main objective of this research is to provide an efficient solution method to generate a synchronized work schedule for the road clearing teams. The solution should specify the synchronized routes of each clearing team so that: 1) connectivity of the network is regained, and 2) none of the closed roads are traversed unless their unblocking/clearing procedure is finished. In this study we develop an exact Mixed Integer Programming (MIP) formulation to solve this problem. Furthermore, we propose a matheuristic that is based on an MIP-relaxation and a local search algorithm. We prove that the optimality gap of the relaxation solution is bounded by K times the lower bound obtained from the relaxed model, where K is the number of teams. We show computationally that the matheuristic obtains optimal or near-optimal solutions.