Cost allocation in collaborative forest transportation

Transportation planning is an important part of the supply chain or wood flow chain in forestry. There are often several forest companies operating in the same region and collaboration between two or more companies is rare. However, there is an increasing interest in collaborative planning as the potential savings are large, often in the range 5-15%. There are several issues to agree on before such collaborative planning can be used in practice. A key question is how the total cost or savings should be distributed among the participants. In this paper, we study a large application in southern Sweden with eight forest companies involved in a collaboration. We investigate a number of sharing mechanisms based on economic models including Shapley value, the nucleolus, separable and non-separable costs, shadow prices and volume weights. We also propose a new allocation method, with the aim that the participants relative profits are as equal as possible. We use two planning models, the first is based on direct flows between supply and demand points and the second includes backhauling. We also study how several time periods and geographical distribution of the supply and demand nodes affect the solutions. Better planning within each company can save about 5% and collaboration can increase this about another 9% to a total of 14%. The proposed allocation method is shown to be a practical approach to share the overall cost/savings.