Scheduling production for a sawmill: A robust optimization approach

Optimization models are increasingly being used for planning natural resources operations. However, the inherent uncertainty present in natural resources makes it difficult to directly apply their results. In particular, production scheduling for sawmills presents several challenges since the supply of logs and the finished product orders are often unknown at scheduling time. In this paper we consider the problem of scheduling production under uncertainty in a sawmill, where the deterministic model proposed by Maturana et al. (2010) was extended to account for uncertainties in product demand and availability of raw materials. The robust optimization methodology of Bertsimas and Sim (2004) and Bertsimas and Thiele (2006) was applied to develop three robust models: one that considers only uncertainty in the product demand, the second considers only uncertainty in the raw material supply, and the third considers both uncertainties simultaneously. For each of these models we carried out an experiment to evaluate the robustness of the solutions and the effect of the conservatism level on the solutions. This allowed us to determine the impact of both sources of uncertainty separately, and the combined effect on the production schedules. In each experiment we defined several levels of variability for the uncertain parameters, and for each of them, we changed the level of conservatism through the manipulation of budgets of uncertainty. We analyzed the behavior of the robust solutions and their average performance with respect to uncertainty using Monte Carlo simulation. This analysis allowed us to provide several managerial insights that could help schedulers choose the appropriate level of conservatism with respect to each source of uncertainty according to their preferences.