The multi-period vehicle routing problem with refueling decisions: Traveling further to decrease fuel cost?

Most vehicle routing approaches disregard the need to refuel fleets. However, planners search for opportunities to refuel at lower prices even if, counter-intuitively, distant fuel stations need to be visited. We propose a novel mathematical formulation and develop branch-and-cut and matheuristic algorithms to efficiently tackle this problem. Results indicate that, to minimize costs, detour distances may increase up to 6 percentage points when fuel stations with lower prices are farther away from the depot. For practice, these insights imply that current policies disregarding station location and/or fuel prices along with "myopic" planning horizons may lead to sub-optimal decisions.