Algorithms for Solving the Crosscutting Problem in a Wood Processing Mill

Abstract

In this thesis, an exact and an inexact method are proposed for solving the crosscutting problem in a wood cutting mill. In a wood cutting mill, boards are first cut along their length (rip) into strips; then the obtained strips are cut along their width (crosscut) into cut-pieces with specific length and demand. Removing the defected areas of wood from the strips gives us clear pieces which must be cut into cut-pieces. The crosscutting problem is the problem of finding cutting patterns for all clear pieces such that demand of all cut-pieces is satisfied with minimum amount of incoming strips.

A Mixed Integer Programming (MIP) model is developed for solving the crosscutting problem optimally; solving the MIP model is, however, very time-consuming. As a result, we added some valid inequalities (VI's) to the model with the purpose of increasing the efficiency of the model. The VI's are useful, but the model still couldn't solve large instances in reasonable time.

To overcome the difficulty of solving time for large instances a heuristic method (inexact method) is proposed for solving the problem. We evaluated the quality of the solution obtained by the heuristic method, and its solving time. The heuristic method is fast enough to solve very large instances; the value of the solution obtained via this heuristic, however, is a few percent above optimal in the instances that we performed the experiment on.