A constructive heuristic for the two dimensional bin packing problem with guillotine cuts and stacked boards

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. Keywords—Bin Packing, combinatorial optimization, heuristics I. Problem description and literature overview Cutting and packing problems have received a lot of attention from reseachers during the last decades, and problem variants are found in many different industries. An early typology can be found in [2], this is improved and extended in [6]. In this paper, we consider a problem from the furniture industry, where parts for tables, shelves, cabinets, etc, are cut from boards of given sizes. According to the typology provided by [6], this problem should be classified as a Cutting Stock Problem if the small items are weakly heterogeneous, and as a Bin Packing Problem if the small items are strongly heterogeneous. The product mix at Grande Fabrikker in Innfjorden, Norway, where the problem presented here is taken from, is a mix of standard products produced in larger batches, and custom made products where the number of equally sized items typically is quite