Conference Proceedings

Abstract

We present a description and a solution algorithm for a new variant of the well-known two-dimensional bin packing problem with guillotine cuts. The problem is taken from the furniture industry, where boards are cut into parts to build cabinets, tables, shelves, etc. One of course wants to make cutting patterns which minimize the amount of waste, but it is also important to save operating time on the saw. This can be done by utilizing the maximum cutting height on the saw by cutting a stack of boards, all with the same cutting pattern, simultaneously. This means that in addition to minimizing waste, one seeks to minimize the number of stacks of boards to be cut by repeating the same cutting patterns a given number of times corresponding to the maximum height of a stack, which again depends on the maximum cutting height of the saw and the thickness of the boards. Computational testing shows that significant amounts of time can be saved without increasing the amount of waste.