An exact approach to minimize the greenhouse gas emissions in timber transport

Received 12 May 2015 Accepted 01 July 2015 Abstract—This paper presents an exact method for solving a multi depot vehicle routing problem with pick-up and delivery and time windows (MDVRPPDTW) for an application within the forest industry. The proposed iterative solution approach is capable of providing a global optimal solution for the MDVRPPDTW in three steps. By relaxing the problem, this method can also be transformed into a heuristic approach that does not guarantee the exact solution. Hence, we denote it as near-exact solution approach (NE). The first step is to solve an extended assignment problem (EAP) that generates a valid network for the log-trucks. Afterwards, feasibility checks concerning the maximum tour length and time windows are performed. Violations lead to the addition of cuts to the EAP. Finally, the third step of the NE is to solve the MDVRPPDTW on the generated constrained network. For the numerical studies, test instances of different scale that are based on real life geographical information have been used. They are solved with the NE and a dynamic Tabu Search strategy that uses an alternating neighborhood (TSAS_dyn). The results show that the NE outperforms the TSAS_dyn for problem sizes up to 60 tasks and 20 trucks. For larger problem instances the metaheuristic should be used, while NE provides valuable lower bounds for TSAS_dyn.