Two Heuristic Algorithms for a Large-Scale Mixed-Integer Production Planning Model with Random Yield and Demand: A Case in Sawmills

This study considers a real-world multi-period, multi-product production planning problem involving set-up constraints, with random yield and demand. The resulting large-scale multi-stage stochastic mixed-integer model cannot be solved by using the mixed-integer solver of a commercial optimization package. The production planning model is a mixed-integer programming (MIP) model without any special structure. As a consequence, developing efficient decomposition and cutting plane algorithms to obtain a good solution in a reasonable amount of time is not straightforward. We use two solution strategies to find good solutions with an acceptable gap to the optimal solution: (1) The first strategy is based on the progressive hedging algorithm (PHA). The solution of this strategy is a local optimum and an upper bound for the optimal objective value of the multi-stage stochastic model. (2) 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 introduce scenario selection rules in order to increase the rate of convergence and the quality of solution. Computational experiments for a real world large-scale sawmill production planning model verify and compare the effectiveness of the two proposed solution strategies in finding quickly good approximate solutions.