A 2D Convex Shapes Bin Packing Problem in the Production of Laminated Safety Glass

Abstract

The discussed two-dimensional nesting problem is motivated by the production of differently shaped tiles of laminated safety glass that can be represented by primitive, convex polygons. Within as few rectangular bins as possible, representing the space of a furnace, tiles must be placed without overlapping. While the primary problem is to minimize the number of occupied bins, distances between adjacent tiles or a tile and an adjacent furnace boundary must be neither too small nor too large to ensure the stability of the furnace filling during a lamination process. To fulfill this condition, a minimum number of additional rectangular support plates must be added. These plates are considered equivalent to tiles when measuring distances. This is a new aspect that, to our knowledge, has not been covered in the literature so far. We represent the problem as a mixed integer linear program based on no-fit polygons and compare results with those of a greedy-type heuristic.