Reducing cardinality in linear programmed cutting stock solutions

Many of the difficulties associated with applications of the linear programming model of cutting stock problems are related firstly to the lack of control over small batch sizes and secondly, although just as seriously, to the excessive numbers of batches (and hence set-ups) with result. Inherent in the approach is also the difficulty of rounding fractional solutions to feasible integer solutions. This paper provides an approach to these difficulties within the framework of the linear programming model. The results reported indicate that the approach provides a very real advance over previously reported algorithms.