A time-dependent vehicle routing problem in multigraph with FIFO property

The classic vehicle routing problems are usually designed with one edge (or arc) between two nodes. However, sometimes, there are situations in which one node can be accessible from another with more than one edge. In this paper, a new extension of the time-dependent vehicle routing problem was studied. In this problem, the existence of more than one edge between the nodes was allowed. This property can be important in competitive markets in order to achieve better and faster product deliveries/services. So, the problem was modeled as the time-dependent vehicle routing problem in multigraph which provided the FIFO property. In addition, a heuristic tabu search (TS) algorithm was proposed to solve the problem, in which neighborhood search was randomly selected among swap or reverse exchanges. Finally, computational results of TS algorithm and exact solution method were represented over forty instances. It was shown that TS was more effective than exact solution method in terms of the quality of results and computational time.