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The social pressure on freight carriers increases to account for emissions caused by their trucks. One way of doing this is to minimize total fuel consumption during vehicle routing. Fuel consumption is directly related to reducing greenhouse gas emissions. However, fuel consumption does not only depend on the driven distances but also on the payload. In this paper, a vehicle routing problem with an unlimited number of heterogeneous vehicles and a fuel consumption-minimization objective function is considered, which was introduced by Kopfer, Schönberger, and Kopfer [9]. It is denoted as EVRP-VC. Till now, the EVRP-VC has only been solved via a commercial solver. Some instances could not be solved within a time limit of 15 minutes. In this paper, a heuristic approach is applied for the first time to the EVRP-VC. An existing column generationbased heuristic is modified. We extend it by a procedure that …