A Simple Model for a Timber Transportation Scheduling Problem

Timber transportation is a major activity in the forest industry and leads to challenging operational research problems. In this work, we study a log-truck scheduling problem inspired by a real case from a Belgian forest company. It aims at designing the weekly schedule for the transportation of timber from harvest to demand points. In this problem, drivers start and end their working day at home and have a limited working time per day. The quantity available in harvest points is typically several truckloads and full truckloads are thus supposed. The cost function is proportional to the total number of working days (by all drivers), and time windows at the harvest and demand points are not included. The characteristics of the case allow us to propose an integer optimization model which is easy to implement and solve. In particular, the model does not include the order in which forests are visited by a driver. While the log-truck scheduling problem is often related to pickup and delivery problems in the literature, the order of the nodes in the route do not have to be included in our modeling, as truck flow balancing is sufficient. When applying our approach to the inspiring case, our model shows to be efficient, finding good solutions (optimality gap of few percent) in a reasonable time (few minutes). The results reveal a significant improvement compared to the actual schedule used by the company.