The Clarke & Wright (C&W) algorithm is one of the most widely used classical heuristics in capacitated Vehicle Routing Problems (VRPs) in which a linear function of distance is considered as the objective function. The C&W algorithm is very simple and easy to implement, and produces fairly good solutions very fast. In this study, the C&W algorithm is adopted for the cumulative VRP with limited duration (CumVRP-LD) where load is also considered in the objective function as well as distance. The most common applications of cumulative VRPs are the determination of routing policies that minimize total fuel consumption. A 2-phase constructive heuristic approach including the K-means clustering algorithm is proposed to improve the computational performance of the modified C&W algorithm for CumVRP-LD. The main contribution of this study is the definition of a new extended formulation that captures truckload and travel distance by considering the unique characteristics of the problem and to develop a fast and easy implemented constructive algorithm for CumVRP-LD. Such approaches are necessary for the development of systems that respond fast, possibly online, to changes in the real problem situations. (C) 2016 Elsevier Ltd. All rights reserved.