A mathheuristic approach for the vehicle routing problem with queuing considerations

Queuing in vehicle routing problems happens when a given node requires to be visited by several vehicles, whereas only a limited number of vehicles can perform the service simultaneously. Hence, some vehicles must wait until the node is available. We present in this paper a mathheuristic approach to solve the problem. This approach incorporates two phases. The first phase executes a rolling horizon heuristic multiple times to generate an initial set of solutions. Those generated solutions are used to initialize a pool of routes. In the second phase, a column-generation based procedure is used to generate new routes. The contribution of our paper can be summarized as follows. (1) We implemented an efficient set partitioning model that allocates pre-determined slots of time to service operations of vehicles. (2) We proposed fast pricing heuristics to generate new routes with negative reduced costs. (3) The newly generated routes are based on existing ones, keeping the same physical description but the starting times of service operations are modified to better fit the queuing aspects. Performance evaluation has been conducted using instances derived from data provided by forest companies. Experiments proved the effectiveness of the proposed approach, by recording low route duration and achieving almost zero queuing times compared to the initial pool of solutions.