Sawmill Production Planning Under Uncertainty: Modelling and Solution Approaches

We investigate the operational level production planning problem in the sawing units of sawmills under the uncertainty in the quality of materials and demand. In order to widen the application of the production planning model in different types of sawmills, we also take into account setup constraints. We propose two-stage stochastic programming, robust optimization, and multistage stochastic programming models to formulate different aspects of this problem. As demand and yield own different uncertain natures, they are modeled separately and then integrated. Demand uncertainty is considered as a dynamic stochastic data process during the planning horizon which is modeled as a scenario tree. The uncertain yield is modeled as scenarios with a stationary probability distribution during the planning horizon. Yield scenarios are then integrated into each node of demand scenario tree, constituting a hybrid scenario tree. We also propose two solution strategies to find good solutions with an acceptable gap to the optimal solution, while taking into account setup constraints in the production planning model. The first strategy is based on the progressive hedging algorithm (PHA), while the second strategy is a successive approximation heuristic which solves the problem by considering only a subset of scenarios which is updated at each iteration. We conduct a case study with respect to a realistic scale prototype sawmill. Computational experiments highlights the effectiveness of the proposed tools for production planning under uncertainty in the sawing units of sawmills.