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 [Gingras, J.-F., Favreau, J., 2002. Incidence du triage sur la productivité des systèmes par bois tronçonnés. Avantage 3], the harvesting cost per unit volume increases as the number of product variety harvested per block increases. The overall product allocation problem is a large scale mixed integer programming problem with the objective of minimizing combined harvesting and aggregated transportation costs, under demand satisfaction constraints. A heuristic is first introduced then, an algorithm based on the branch-and-price approach is proposed for larger scale problems. 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.