A scenario decomposition approach for stochastic production planning in sawmills

M Kazemi Zanjani, M Nourelfath and D Ait-Kadi
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M Kazemi Zanjani: 1] Concordia University, Montreal, Canada[2] Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montreal, Canada
M Nourelfath: 1] Université Laval, Québec, Canada[2] Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montreal, Canada
D Ait-Kadi: 1] Université Laval, Québec, Canada[2] Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT), Montreal, Canada

Journal of the Operational Research Society, 2013, vol. 64, issue 1, 48-59

Abstract: 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.

Date: 2013
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