A mathematical modeling for simultaneous routing and scheduling of logging trucks in the forest supply chain

Transportation cost in the forest industry highly impacts on the overall costs of the supply chain, and therefore it must be optimized for improving profitability. Considering the problem characteristics, the decisions related to the transport problem, such as allocation, routing, and scheduling, are usually decoupled, resorting to different decomposition strategies. As a result, suboptimal and underperforming solutions are obtained. In this article, decisions about raw material allocation, routing and scheduling are simultaneously solved through a mixed integer linear programming model. The proposed model involves an arc-based formulation for routing and a time grid discretization, including the definition of loading and unloading shifts for scheduling. This leads to detailed transportation planning for a homogeneous logging truck fleet that must fulfill the demand of varied raw material at minimum cost. Examples and performance tests are provided to assess the capabilities of the proposed exact approach.