A Multi-Stage Stochastic Programming Approach for Production Planning with Uncertainty in the Quality of Raw Materials and Demand

Motivated by the challenges encountered in sawmill production planning, we study a multi-product, multi-period production planning problem with uncertainty in the quality of raw materials and consequently in processes yields, as well as uncertainty in products demands. 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. Each stage in demand scenario tree corresponds to a cluster of time periods, for which the demand has a stationary behavior. The uncertain yield is modeled as scenarios with a stationary probability distribution during the planning horizon. Yield scenarios are then integrated in each node of demand scenario tree, constituting a hybrid scenario tree. Based on the hybrid scenario tree for the uncertain yield and demand, a multi-stage stochastic programming (MSP) model is proposed which is full recourse for demand scenarios and simple recourse for yield scenarios. We conduct a case study with respect to a realistic scale sawmill. Numerical results indicate that the solution to the multi-stage model is far superior to the optimal solution to the mean-value deterministic and the twostage stochastic models.