Integrated tactical planning in the lumber supply chain under demand and supply uncertainty

Lumber supply chain includes forests as suppliers, sawmills as production sites, distribution centers, and different types of customers. In this industry, the raw materials are logs that are shipped from forest contractors to sawmills. Logs are then sawn to green/finished lumbers in sawmills and are distributed to the lumber market through different channels. Unlike a traditional manufacturing industry, the lumber industry is characterized by a divergent product structure with the highly heterogeneous nature of its raw material (logs). Moreover, predicting the exact amount of the product demand and the availability of logs in the forest is impossible in this industry. Thus, considering random demand and supply in the lumber supply chain planning is essential. Integrated tactical planning in a supply chain incorporates the synchronized planning of procurement, production, distribution and sale activities in order to ensure that the customer demand is satisfied by the right product at the right time. Briefly, in this dissertation, we aim at developing integrated planning tools in lumber supply chains for making decisions in harvesting, material procurement, production, distribution, and sale activities in order to obtain a maximum robust profit and service level in the presence of uncertainty in the log supply and product demand. In order to gain the latter objectives, we can categorize this research into three phases. In the first phase, we investigate the integrated annual planning of harvesting, procurement, production, distribution, and sale activities in the lumber supply chain in a deterministic context. The problem is formulated as a mixed integer programming (MIP) model. The proposed model is applied on a real-size case study, which leads to a large-scale MIP model that cannot be solved by commercial solvers in a reasonable time. Consequently, we propose a Lagrangian Relaxation based heuristic algorithm in order to solve the latter MIP model. While improving significantly the convergence, the proposed algorithm also guarantees the feasibility of the converged solution. In the second phase, the uncertainty is incorporated in the lumber supply chain tactical planning problems. Thus, we propose a multi-stage stochastic mixed-integer programming (MS-MIP) model to address this problem. Due to the complexity of solving the latter MS-MIP model with commercial solvers or relevant solution methodologies in the literature, we develop a Hybrid Scenario Cluster Decomposition (HSCD) heuristic algorithm which is also amenable to parallelization. This algorithm decomposes the original scenario tree into a set of smaller sub-trees. Hence, the MS-MIP model is decomposed into smaller sub-models that are coordinated by Lagrangian terms in their objective functions. By embedding an ad-hoc heuristic and a Variable Fixing algorithm into the HSCD algorithm, we considerably improve its convergence and propose an implementable solution in a reasonable CPU time. Finally, due to the computational complexity of multi-stage stochastic programming approach, we confine our formulation to the robust optimization method. Hence, at the third phase of this research, we propose a robust planning model formulated based on cardinality-constrained method. The latter provides some insights into the adjustment of the level of robustness of the proposed plan over the planning horizon and protection against uncertainty. An extensive set of experiments based on Monte-Carlo simulation is also conducted in order to better validate the proposed robust optimization approach applied on the harvesting planning in lumber supply chains.