Real-time vehicle rerouting problems with time windows

This paper introduces and studies real-time vehicle rerouting problems with time windows, applicable to delivery and/or pickup services that undergo service disruptions due to vehicle breakdowns. In such problems, one or more vehicles need to be rerouted, in real-time, to perform uninitiated services, with the objective to minimize a weighted sum of operating, service cancellation and route disruption costs. A Lagrangian relaxation based-heuristic is developed, which includes an insertion based-algorithm to obtain a feasible solution for the primal problem. A dynamic programming based algorithm solves heuristically the shortest path problems with resource constraints that result from the Lagrangian relaxation. Computational experiments show that the developed Lagrangian heuristic performs very well.