Multi-commodity supply network planning in the forest supply chain

We consider in this paper a two echelon timber procurement system in which the first echelon consists of multiple harvesting blocks and the second echelon consists of multiple mills (e.g., sawmills), both distributed geographically. Demand is put forward by mills in the form of volumes of logs of specific length and species. Due to the impact of log handling and sorting on cut-to-length harvester and forwarder productivity ((15)), the total harvesting cost function increases non-linearly as the number of product harvested per block increases. The overall decision problem is a large scale mixed integer programming problem with the objective of minimizing combined harvesting and aggregated transportation costs, while satisfying demand. We first propose an algorithm based on the dynamic programming approach for a special case of this problem. Then, we propose another fast heuristic algorithm for the general case. An algorithm based on the branch-and-price approach is finally proposed for larger scale problems and comparison. Experimentations compare solutions found with the heuristic with the corresponding optimal solutions obtained with both Cplex (using the branch-and-bound approach) and the branch-and-price approach. Results demonstrate the good performance level of the heuristic approach for small scale problems, and of the branch-and-price approach for large scale problems.