Backhauling in forest transportation: models, methods, and practical usage

In this paper, we consider a tactical transportation planning problem in forestry to decide the destination of logs. This problem is generally solved by finding the flow between a set of supply points and demand points. It can be formulated as a linear programming problem involving direct flows between supply and demand points. However, better solutions can be found by using additional flow variables representing flow in potential backhaul routes. However, the number of such variables is often very large. In this article, we provide the basis for backhaul flow planning in forestry. This includes defining the underlying operations research models for both the flow problem and the subproblem to find backhaul routes. The size of the problem in terms of the number of variables increases rapidly with the number of supplies and demands and we describe a column generation approach for its solution. We report on some case studies and industrial systems where the approach has been used.