A deterministic harvest scheduler using perfect bin-packing theorem

The use of heuristic techniques in forest planning has been promoted by the need to solve complex problems that cannot be solved using mixed integer programming. We proved that for merchantability standards ensuring the perfect bin-packing theorem (PBPT), the maximum volume that can be harvested annually equals the sum of the maximum MAI of the stands. The method accommodates optimality criteria at the stand level, regarded as maximum MAI, and at the forest level, regarded as maximum annual allowable cut. We scheduled the harvesting by adjusting the first fit decreasing algorithm (FFD) to the PBPT conditions. When PBPT conditions were not met, we developed a mixed integer programming solution to adjust the merchantability standards of the stands to the distributional requirements of the PBPT, an adjustment that ensured the optimal performance of the FFD. The adjusted FFD was compared with linear programming (LP) and simulated annealing (SA) using two harvesting ages (i.e., one based on MAI maximization and one determined as the minimal age) and the same set of spatial temporal constraints for three areas in north-eastern British Columbia, Canada. We found that the adjusted FFD performed 100 times faster than SA and for annual allowable cut (AAC) supplied results that were more homogenous and at least 10% greater than the AAC supplied by SA. Furthermore, the adjusted FFD seemed to be relatively insensitive to spatial constraints (i.e., adjacency), while SA displayed a 70% reduction in AAC in response to an increase in adjacency delay from 1 year to 20 years. The results suggest that both adjusted FFD and SA are impacted by the selection of the harvesting age, but the adjusted FFD could still outperform SA.