Distance-constrained capacitated vehicle routing problems with flexible assignment of start and end depots

This paper proposes two new distance-constrained capacitated vehicle routing problems (DCVRPs) to investigate for the first time, and study potential benefits in flexibly assigning start and end depots. The first problem, DCVRP_Fix is an extension of the traditional symmetric DCVRP, with additional service and travel time constraints, minimization of the number of vehicles and flexible application to both symmetric and asymmetric problems. The second problem, DCVRP_Flex is a relaxation of DCVRP_Fix to enable the flexible assignment of start and end depots. This allows vehicles the freedom to start and end their tour at different depots, while allowing for intermediate visits to any depot (for reloading) during the tour. Network models, integer programming formulations and solution algorithms for both problems are developed and presented in this paper. An analytical comparison of both problems is carried out with Singapore as a case study, considering the impact of depot locations and problem symmetry using four cases. Results show a generation of cost savings up to 49.1% by DCVRP_Flex across all the four cases. A significant portion of this stems from the flexibility to reload at any depot while the rest of it is derived from the flexibility to return to any depot. DCVRP_Flex's adaptability and superior performance over DCVRP_Fix provides strong motivation for further research on improved exact algorithms and heuristics for this problem.