Setup and Open-Stacks Minimization in One-Dimensional Stock Cutting

The primary objective in cutting and packing problems is trim loss or material input minimization (in stock cutting) or value maximization (when packing into a knapsack). However, in real-life production we usually have many other objectives (costs) and constraints. Probably the most complex auxiliary criteria of a solution are the number of different cutting patterns (setups) and the maximum number of open stacks during the cutting process. There are applications where the number of stacks is restricted to two. We design a sequential heuristic to minimize material input while restricting the number of open stacks to any given limit. Then, the heuristic is simplified and integrated into a setup minimization approach in order to combine setup and open stacks minimization. To get a smaller number of open stacks, we may split up the problem into several parts of smaller dimension. Different solutions are evaluated in relation to the multiple objectives using the PARETO criterion. Finally we extend some known models by boolean variables that account for the states of stacks in the cutting sequence.