A scenario decomposition approach for stochastic production planning in sawmills

This study considers a real world stochastic multi‐period, multi‐product production planning problem. Motivated by the challenges encountered in sawmill production planning, the proposed model takes into account two important aspects: (i) randomness in yield and in demand; and (ii) set‐up constraints. Rather than considering a single source of randomness, or ignoring set‐up constraints as is typically the case in the literature, we retain all these characteristics while addressing real life‐size instances of the problem. Uncertainties are modelled by a scenario tree in a multi‐stage environment. In the case study, the resulting large‐scale multi‐stage stochastic mixed‐integer model cannot be solved by using the mixed‐integer solver of a commercial optimization package, such as CPLEX. Moreover, as the production planning model under discussion is a mixed‐integer programming model lacking any special structure, the development of decomposition and cutting plane algorithms to obtain good solutions in a reasonable time‐frame is not straightforward. We develop a scenario decomposition approach based on the progressive hedging algorithm, which iteratively solves the scenarios separately. CPLEX is then used for solving the sub‐problems generated for each scenario. The proposed approach attempts to gradually steer the solutions of the sub‐problems towards an implementable solution by adding some penalty terms in the objective function used when solving each scenario. Computational experiments for a real‐world large‐scale sawmill production planning model show the effectiveness of the proposed solution approach in finding good approximate solutions.