Multi-period vehicle routing problem with recurring dynamic time windows

This paper discusses a new practical variant of the vehicle routing problem with time windows (VRPTW), which originated from the regional transportation planning for oil products at a China National Petroleum Corporation (CNPC) branch in a northwest province of mainland China. Tanker trucks are scheduled to serve each oil station in multiple periods according to a recurring and dynamic time window setting. Refilling at an oil depot is always required after visiting an oil station, so it is safe to assume that the vehicles are uncapacitated. The problem is formulated into a mixed-integer programming model and shown to be NP-Hard. We found that the mixed-integer programming model is only solvable for very small impractical cases using exact methods, e.g., branch and cut, which is employed by the state-of-the-art commercial solver ILOG CPLEX. Moreover, due to the floating time windows imposed on the nodes, traditional local search-based heuristics with node interchange operators are not applicable. Thus, we adapt and propose an iterative time window partitioning heuristic that discretizes time windows into multiple time points with dynamic partition widths. Experiments show good quality solutions can be achieved for problem cases with practical sizes.