A tabu search heuristic for the heterogeneous vehicle routing problem on a multigraph

•We model a time-constrained heterogeneous vehicle routing problem on a multigraph.•We develop a tabu search heuristic that efficiently handles the parallel arcs.•We show the flexibility in route construction on the multigraph.•Utilizing parallel arcs, cost savings on the order of 5% are obtained in the tests.

We study a time-constrained heterogeneous vehicle routing problem on a multigraph where parallel arcs between pairs of vertices represent different travel options based on criteria such as time, cost, and distance. We formulate the problem as a mixed-integer linear programming model and develop a tabu search heuristic that efficiently addresses computational challenges due to parallel arcs. Numerical experiments show that the heuristic is highly effective and that freight operators can achieve advantages in cost and customer service by considering alternative paths, especially when route duration limits are restrictive and/or when vehicles of smaller capacity are dispatched to serve remote customers.