Backhauling in forest transportation : models, methods and practical usage

Transportation planning in forestry is divided into strategic, tactical and operational depending on the length of the planning horizon. We consider a tactical problem of finding efficient backhauling routes. Given a set of supply and demand points the backhauling problem is to identify a set of efficient routes which is a combination of direct tours between supply and demand points such that the unloaded distance is minimized. Given these routes we formulate a linear programming problem where the solution is the actual flows in the routes. The problem normally has a time horizon ranging from one to five weeks. However, in some cases it can be included in strategic planning for more than one year and as a basis for daily operative route planning. The size of the problem increases rapidly with the number of supplies and demands and we describe a column generation approach for its solution. Models and methods have been used with success in a number of case studies and in decision support systems. We describe the model and solution method and report on case studies and systems where the approach has been used.