Combined primary and secondary log breakdown optimisation

At sawmills logs are converted into boards by a series of cutting operations. Primary cuts reduce logs into slabs of wood, secondary cuts produce boards. Boards incorporating natural defects such as knots (branch sections) are inferior to clear boards. The aim of the sawmill is to cut logs to produce boards of greatest value. However, when logs are pruned, knots are only exposed after primary cutting. This complicates the conversion problem. To effectively convert logs into boards the interrelated effects of the cutting phases must be recognized. In this paper linked dynamic programming formulations are developed. The inner (secondary) formulation determines the optimal sequence for cutting a slab into boards. The result is passed to the master (primary) formulation that determines the optimal sequence for cutting the log into slabs. The objective functions can be modified to maximise either total value of boards (incorporating quality) or total volume. Results from simulations indicate that significant increases in value are possible when quality is considered.