Vehicle routing with cumulative objectives: A state of the art and analysis

•Vehicle routing with cumulative objectives.•Feature-based cumulative VRPs scheme.•CumVRP and CCVRP approaches analysis.•Cumulative VRP benchmark instances mapping. In the past decades, there has been an increasing body of research in vehicle routing problems involving cumulative costs. These problems consider cumulative objective functions such as the sum of arrival times to customers or the cumulative costs based on the vehicles’ load throughout the routes. This paper reviews this type of routing problem by means of the cumulative vehicle routing problem (Cum-VRP) and cumulative capacitated vehicle routing problem (CCVRP). In doing so, we present and discuss all related problem variants with regard to the different problem features proposed over time. Moreover, we provide an analysis of related papers concerning solution algorithms and used benchmark instances. Finally, an overview of the trends and promising areas for further research are also provided.