Solving the time-dependent multi-trip vehicle routing problem with time windows and an improved travel speed model by a hybrid solution algorithm

In this study, we explore a time-dependent multi-trip vehicle routing problem (TDMTVRP) with an improved travel speed model. This problem is set in a scenario that (a) a set of customers with fixed demands and service time windows have to be served in a sequence of service trips which originate and terminate at a distribution centre, (b) the service trips will be assigned to a fleet of vehicles with fixed capacities and maximum allowable working durations each day, (c) each vehicle can perform more than one service trip, and (d) the link travel times varies with vehicle travel speeds which results from congestion effects during different time of day in urban areas. The aim of the TDMTVRP model is to find an optimal strategy to minimize the vehicle utilized times and their total scheduling time. A continuous piecewise linear function is first introduced to represent the variation and transition of vehicle travel speeds with the time of the day instead of the traditional staircase travel speed function. Then a hybrid solution algorithm is developed by using the nearest-neighbour heuristic to obtain an initial solution and Tabu search heuristic to search the optimal solution. Finally, an experimental case study is used to verify the feasibility of the proposed model and algorithm. The experimental results indicate that compared with the CVRPTW (capacitated vehicle routing problem with time windows) model, the TDMTVRP model proposed in this study can both decrease the vehicle utilized times dramatically and shorten the vehicle travel distances slightly in dealing with the vehicle routing problem.