0000000001035161
AUTHOR
Antonio Martinez-sykora
Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts
Abstract This paper presents an approach for solving a new real problem in cutting and packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cutting and packing problems that include guillotine cuts deal with rectangles only, where all cuts are orthogonal to the edges of the stock sheet and a maximum of two angles of rotation are permitted. The literature tackling packing problems with irregular shapes largely focuses on strip packing i…
The Steiner Traveling Salesman Problem and its extensions
Abstract This paper considers the Steiner Traveling Salesman Problem, an extension of the classical Traveling Salesman Problem on an incomplete graph where not all vertices have demand. Some extensions including several depots or location decisions are introduced, modeled and solved. A compact integer linear programming formulation is proposed for each problem, where the routes are represented with two-index decision variables, and parity conditions are modeled using cocircuit inequalities. Exact branch-and-cut algorithms are developed for all formulations. Computational results obtained confirm the good performance of the algorithms. Instances with up to 500 vertices are solved optimally.
Matheuristics for the irregular bin packing problem with free rotations
[EN] We present a number of variants of a constructive algorithm able to solve a wide variety of variants of the Two-Dimensional Irregular Bin Packing Problem (2DIBPP). The aim of the 2DIBPP is to pack a set of irregular pieces, which may have concavities, into stock sheets (bins) with fixed dimensions in such a way that the utilization is maximized. This problem is inspired by a real application from a ceramic company in Spain. In addition, this problem arises in other industries such as the garment industry or ship building. The constructive procedure presented in this paper allows both free orientation for the pieces, as in the case of the ceramic industry, or a finite set of orientation…